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b/tesi/galla/tesi.bbl @@ -0,0 +1,180 @@ +\begin{thebibliography}{10} + +\bibitem{AmparoreDBGM17} +{\sc Amparore, E.~G., Donatelli, S., Beccuti, M., Garbi, G., and Miner, A.~S.} +\newblock Decision diagrams for petri nets: Which variable ordering? +\newblock In {\em Proceedings of the International Workshop on Petri Nets and + Software Engineering (PNSE'17), co-located with the38th International + Conference on Application and Theory of Petri Nets and Concurrency Petri Nets + 2017 and the 17th International Conference on Application of Concurrency to + System Design {ACSD} 2017, Zaragoza, Spain, June 25-30, 2017\/} (2017), + D.~Moldt, L.~Cabac, and H.~R{\"{o}}lke, Eds., vol.~1846 of {\em {CEUR} + Workshop Proceedings}, CEUR-WS.org, pp.~31--50. + +\bibitem{BabarBDM10} +{\sc Babar, J., Beccuti, M., Donatelli, S., and Miner, A.~S.} +\newblock Greatspn enhanced with decision diagram data structures. +\newblock In {\em Applications and Theory of Petri Nets, 31st International + Conference, {PETRI} {NETS} 2010, Braga, Portugal, June 21-25, 2010. + Proceedings\/} (2010), J.~Lilius and W.~Penczek, Eds., vol.~6128 of {\em + Lecture Notes in Computer Science}, Springer, pp.~308--317. + +\bibitem{BabarM10} +{\sc Babar, J., and Miner, A.~S.} +\newblock Meddly: Multi-terminal and edge-valued decision diagram library. +\newblock In {\em {QEST} 2010, Seventh International Conference on the + Quantitative Evaluation of Systems, Williamsburg, Virginia, USA, 15-18 + September 2010\/} (2010), {IEEE} Computer Society, pp.~195--196. + +\bibitem{BiereCCZ99} +{\sc Biere, A., Cimatti, A., Clarke, E.~M., and Zhu, Y.} +\newblock Symbolic model checking without bdds. +\newblock In {\em Tools and Algorithms for Construction and Analysis of + Systems, 5th International Conference, {TACAS} '99, Held as Part of the + European Joint Conferences on the Theory and Practice of Software, ETAPS'99, + Amsterdam, The Netherlands, March 22-28, 1999, Proceedings\/} (1999), + R.~Cleaveland, Ed., vol.~1579 of {\em Lecture Notes in Computer Science}, + Springer, pp.~193--207. + +\bibitem{BolligW96} +{\sc Bollig, B., and Wegener, I.} +\newblock Improving the variable ordering of obdds is np-complete. +\newblock {\em {IEEE} Trans. Computers 45}, 9 (1996), 993--1002. + +\bibitem{Bryant86} +{\sc Bryant, R.~E.} +\newblock Graph-based algorithms for boolean function manipulation. +\newblock {\em {IEEE} Trans. Computers 35}, 8 (1986), 677--691. + +\bibitem{CimattiCGGPRST02} +{\sc Cimatti, A., Clarke, E.~M., Giunchiglia, E., Giunchiglia, F., Pistore, M., + Roveri, M., Sebastiani, R., and Tacchella, A.} +\newblock Nusmv 2: An opensource tool for symbolic model checking. +\newblock In {\em Computer Aided Verification, 14th International Conference, + {CAV} 2002,Copenhagen, Denmark, July 27-31, 2002, Proceedings\/} (2002), + E.~Brinksma and K.~G. Larsen, Eds., vol.~2404 of {\em Lecture Notes in + Computer Science}, Springer, pp.~359--364. + +\bibitem{Clarke08} +{\sc Clarke, E.~M.} +\newblock The birth of model checking. +\newblock In {\em 25 Years of Model Checking - History, Achievements, + Perspectives\/} (2008), O.~Grumberg and H.~Veith, Eds., vol.~5000 of {\em + Lecture Notes in Computer Science}, Springer, pp.~1--26. + +\bibitem{ClarkeE81} +{\sc Clarke, E.~M., and Emerson, E.~A.} +\newblock Design and synthesis of synchronization skeletons using + branching-time temporal logic. +\newblock In {\em Logics of Programs, Workshop, Yorktown Heights, New York, + USA, May 1981\/} (1981), D.~Kozen, Ed., vol.~131 of {\em Lecture Notes in + Computer Science}, Springer, pp.~52--71. + +\bibitem{ClarkeES86} +{\sc Clarke, E.~M., Emerson, E.~A., and Sistla, A.~P.} +\newblock Automatic verification of finite-state concurrent systems using + temporal logic specifications. +\newblock {\em {ACM} Trans. Program. Lang. Syst. 8}, 2 (1986), 244--263. + +\bibitem{ClarkeGH97} +{\sc Clarke, E.~M., Grumberg, O., and Hamaguchi, K.} +\newblock Another look at {LTL} model checking. +\newblock {\em Formal Methods in System Design 10}, 1 (1997), 47--71. + +\bibitem{EmersonH86} +{\sc Emerson, E.~A., and Halpern, J.~Y.} +\newblock "sometimes" and "not never" revisited: on branching versus linear + time temporal logic. +\newblock {\em J. {ACM} 33}, 1 (1986), 151--178. + +\bibitem{FernandezMJJ92} +{\sc Fernandez, J., Mounier, L., Jard, C., and J{\'{e}}ron, T.} +\newblock On-the-fly verification of finite transition systems. +\newblock {\em Formal Methods in System Design 1}, 2/3 (1992), 251--273. + +\bibitem{Holzmann97} +{\sc Holzmann, G.~J.} +\newblock The model checker {SPIN}. +\newblock {\em {IEEE} Trans. Software Eng. 23}, 5 (1997), 279--295. + +\bibitem{HolzmannPy96} +{\sc Holzmann, G.~J., Peled, D.~A., and Yannakakis, M.} +\newblock On nested depth first search. +\newblock In {\em The Spin Verification System, Proceedings of a {DIMACS} + Workshop, New Brunswick, New Jersey, USA, August, 1996\/} (1996), + J.~Gr{\'{e}}goire, G.~J. Holzmann, and D.~A. Peled, Eds., vol.~32 of {\em + {DIMACS} Series in Discrete Mathematics and Theoretical Computer Science}, + {DIMACS/AMS}, pp.~23--31. + +\bibitem{MDD} +{\sc Kam, T., Villa, T., and Brayton, R.} +\newblock Multi-valued decision diagrams: Theory and applications," + multiple-valued logic. +\newblock {\em Multiple-Valued Logic 4\/} (01 1998). + +\bibitem{KantLMPBD15} +{\sc Kant, G., Laarman, A., Meijer, J., van~de Pol, J., Blom, S., and van Dijk, + T.} +\newblock Ltsmin: High-performance language-independent model checking. +\newblock In {\em Tools and Algorithms for the Construction and Analysis of + Systems - 21st International Conference, {TACAS} 2015, Held as Part of the + European Joint Conferences on Theory and Practice of Software, {ETAPS} 2015, + London, UK, April 11-18, 2015. Proceedings\/} (2015), C.~Baier and + C.~Tinelli, Eds., vol.~9035 of {\em Lecture Notes in Computer Science}, + Springer, pp.~692--707. + +\bibitem{Keller76} +{\sc Keller, R.~M.} +\newblock Formal verification of parallel programs. +\newblock {\em Commun. {ACM} 19}, 7 (1976), 371--384. + +\bibitem{Lamport80} +{\sc Lamport, L.} +\newblock "sometime" is sometimes "not never" - on the temporal logic of + programs. +\newblock In {\em Conference Record of the Seventh Annual {ACM} Symposium on + Principles of Programming Languages, Las Vegas, Nevada, USA, January 1980\/} + (1980), P.~W. Abrahams, R.~J. Lipton, and S.~R. Bourne, Eds., {ACM} Press, + pp.~174--185. + +\bibitem{SymbMC} +{\sc McMillan, K.~L.} +\newblock {\em Symbolic model checking}. +\newblock Kluwer, 1993. + +\bibitem{Peled96} +{\sc Peled, D.~A.} +\newblock Combining partial order reductions with on-the-fly model-checking. +\newblock {\em Formal Methods in System Design 8}, 1 (1996), 39--64. + +\bibitem{Pnueli77} +{\sc Pnueli, A.} +\newblock The temporal logic of programs. +\newblock In {\em 18th Annual Symposium on Foundations of Computer Science, + Providence, Rhode Island, USA, 31 October - 1 November 1977\/} (1977), {IEEE} + Computer Society, pp.~46--57. + +\bibitem{Sistlac85} +{\sc Sistla, A.~P., and Clarke, E.~M.} +\newblock The complexity of propositional linear temporal logics. +\newblock {\em J. {ACM} 32}, 3 (1985), 733--749. + +\bibitem{DijkP17} +{\sc van Dijk, T., and van~de Pol, J.} +\newblock Sylvan: multi-core framework for decision diagrams. +\newblock {\em {STTT} 19}, 6 (2017), 675--696. + +\bibitem{Vardi95} +{\sc Vardi, M.~Y.} +\newblock An automata-theoretic approach to linear temporal logic. +\newblock In {\em Logics for Concurrency - Structure versus Automata (8th Banff + Higher Order Workshop, Banff, Canada, August 27 - September 3, 1995, + Proceedings)\/} (1995), F.~Moller and G.~M. Birtwistle, Eds., vol.~1043 of + {\em Lecture Notes in Computer Science}, Springer, pp.~238--266. + +\bibitem{VardiW94} +{\sc Vardi, M.~Y., and Wolper, P.} +\newblock Reasoning about infinite computations. +\newblock {\em Inf. Comput. 115}, 1 (1994), 1--37. + +\end{thebibliography} diff --git a/tesi/galla/tesi.bib b/tesi/galla/tesi.bib new file mode 100644 index 0000000..bcc91ff --- /dev/null +++ b/tesi/galla/tesi.bib @@ -0,0 +1,664 @@ +@inproceedings{Pnueli77, + author = {Amir Pnueli}, + title = {The Temporal Logic of Programs}, + booktitle = {18th Annual Symposium on Foundations of Computer Science, Providence, + Rhode Island, USA, 31 October - 1 November 1977}, + pages = {46--57}, + year = {1977}, + crossref = {DBLP:conf/focs/FOCS18}, + url = {https://doi.org/10.1109/SFCS.1977.32}, + doi = {10.1109/SFCS.1977.32}, + timestamp = {Wed, 16 Oct 2019 14:14:54 +0200}, + biburl = {https://dblp.org/rec/bib/conf/focs/Pnueli77}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@proceedings{DBLP:conf/focs/FOCS18, + title = {18th Annual Symposium on Foundations of Computer Science, Providence, + Rhode Island, USA, 31 October - 1 November 1977}, + publisher = {{IEEE} Computer Society}, + year = {1977}, + url = {https://ieeexplore.ieee.org/xpl/conhome/4567914/proceeding}, + timestamp = {Wed, 16 Oct 2019 14:14:54 +0200}, + biburl = {https://dblp.org/rec/bib/conf/focs/FOCS18}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{ClarkeE81, + author = {Edmund M. Clarke and + E. Allen Emerson}, + title = {Design and Synthesis of Synchronization Skeletons Using Branching-Time + Temporal Logic}, + booktitle = {Logics of Programs, Workshop, Yorktown Heights, New York, USA, May + 1981}, + pages = {52--71}, + year = {1981}, + crossref = {DBLP:conf/lop/1981}, + url = {https://doi.org/10.1007/BFb0025774}, + doi = {10.1007/BFb0025774}, + timestamp = {Tue, 14 May 2019 10:00:52 +0200}, + biburl = {https://dblp.org/rec/bib/conf/lop/ClarkeE81}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@proceedings{DBLP:conf/lop/1981, + editor = {Dexter Kozen}, + title = {Logics of Programs, Workshop, Yorktown Heights, New York, USA, May + 1981}, + series = {Lecture Notes in Computer Science}, + volume = {131}, + publisher = {Springer}, + year = {1982}, + url = {https://doi.org/10.1007/BFb0025769}, + doi = {10.1007/BFb0025769}, + isbn = {3-540-11212-X}, + timestamp = {Tue, 14 May 2019 10:00:52 +0200}, + biburl = {https://dblp.org/rec/bib/conf/lop/1981}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{EmersonH86, + author = {E. Allen Emerson and + Joseph Y. Halpern}, + title = {"Sometimes" and "Not Never" revisited: on branching versus linear + time temporal logic}, + journal = {J. {ACM}}, + volume = {33}, + number = {1}, + pages = {151--178}, + year = {1986}, + url = {https://doi.org/10.1145/4904.4999}, + doi = {10.1145/4904.4999}, + timestamp = {Tue, 06 Nov 2018 12:51:44 +0100}, + biburl = {https://dblp.org/rec/bib/journals/jacm/EmersonH86}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{Lamport80, + author = {Leslie Lamport}, + title = {"Sometime" is Sometimes "Not Never" - On the Temporal Logic of Programs}, + booktitle = {Conference Record of the Seventh Annual {ACM} Symposium on Principles + of Programming Languages, Las Vegas, Nevada, USA, January 1980}, + pages = {174--185}, + year = {1980}, + crossref = {DBLP:conf/popl/1980}, + url = {https://doi.org/10.1145/567446.567463}, + doi = {10.1145/567446.567463}, + timestamp = {Tue, 06 Nov 2018 11:07:43 +0100}, + biburl = {https://dblp.org/rec/bib/conf/popl/Lamport80}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@proceedings{DBLP:conf/popl/1980, + editor = {Paul W. Abrahams and + Richard J. Lipton and + Stephen R. Bourne}, + title = {Conference Record of the Seventh Annual {ACM} Symposium on Principles + of Programming Languages, Las Vegas, Nevada, USA, January 1980}, + publisher = {{ACM} Press}, + year = {1980}, + url = {http://dl.acm.org/citation.cfm?id=567446}, + isbn = {0-89791-011-7}, + timestamp = {Mon, 21 May 2012 16:19:49 +0200}, + biburl = {https://dblp.org/rec/bib/conf/popl/1980}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@book{SymbMC, + author = {Kenneth L. McMillan}, + title = {Symbolic model checking}, + publisher = {Kluwer}, + year = {1993}, + url = {https://doi.org/10.1007/978-1-4615-3190-6}, + doi = {10.1007/978-1-4615-3190-6}, + isbn = {978-0-7923-9380-1}, + timestamp = {Tue, 23 Jul 2019 12:44:35 +0200}, + biburl = {https://dblp.org/rec/bib/books/daglib/0071856}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{Keller76, + author= {Robert M. Keller}, + title = {Formal Verification of Parallel Programs}, + journal = {Commun. {ACM}}, + volume = {19}, + number = {7}, + pages = {371--384}, + year = {1976}, + url = {https://doi.org/10.1145/360248.360251}, + doi = {10.1145/360248.360251}, + timestamp = {Tue, 06 Nov 2018 12:51:40 +0100}, + biburl = {https://dblp.org/rec/bib/journals/cacm/Keller76}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{SistlaC85, + author = {A. Prasad Sistla and + Edmund M. Clarke}, + title = {The Complexity of Propositional Linear Temporal Logics}, + journal = {J. {ACM}}, + volume = {32}, + number = {3}, + pages = {733--749}, + year = {1985}, + url = {https://doi.org/10.1145/3828.3837}, + doi = {10.1145/3828.3837}, + timestamp = {Wed, 14 Nov 2018 10:35:24 +0100}, + biburl = {https://dblp.org/rec/bib/journals/jacm/SistlaC85}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{Holzmann97, + author = {Gerard J. Holzmann}, + title = {The Model Checker {SPIN}}, + journal = {{IEEE} Trans. Software Eng.}, + volume = {23}, + number = {5}, + pages = {279--295}, + year = {1997}, + url = {https://doi.org/10.1109/32.588521}, + doi = {10.1109/32.588521}, + timestamp = {Wed, 17 May 2017 10:56:37 +0200}, + biburl = {https://dblp.org/rec/bib/journals/tse/Holzmann97}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{SPOT2, + author = {Alexandre Duret{-}Lutz and + Alexandre Lewkowicz and + Amaury Fauchille and + Thibaud Michaud and + Etienne Renault and + Laurent Xu}, + title = {Spot 2.0 - {A} Framework for {LTL} and {\textbackslash}omega -Automata + Manipulation}, + booktitle = {Automated Technology for Verification and Analysis - 14th International + Symposium, {ATVA} 2016, Chiba, Japan, October 17-20, 2016, Proceedings}, + pages = {122--129}, + year = {2016}, + crossref = {DBLP:conf/atva/2016}, + url = {https://doi.org/10.1007/978-3-319-46520-3\_8}, + doi = {10.1007/978-3-319-46520-3\_8}, + timestamp = {Tue, 14 May 2019 10:00:49 +0200}, + biburl = {https://dblp.org/rec/bib/conf/atva/Duret-LutzLFMRX16}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@proceedings{DBLP:conf/atva/2016, + editor = {Cyrille Artho and + Axel Legay and + Doron Peled}, + title = {Automated Technology for Verification and Analysis - 14th International + Symposium, {ATVA} 2016, Chiba, Japan, October 17-20, 2016, Proceedings}, + series = {Lecture Notes in Computer Science}, + volume = {9938}, + year = {2016}, + url = {https://doi.org/10.1007/978-3-319-46520-3}, + doi = {10.1007/978-3-319-46520-3}, + isbn = {978-3-319-46519-7}, + timestamp = {Tue, 14 May 2019 10:00:49 +0200}, + biburl = {https://dblp.org/rec/bib/conf/atva/2016}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{HolzmannPY96, + author = {Gerard J. Holzmann and + Doron A. Peled and + Mihalis Yannakakis}, + title = {On nested depth first search}, + booktitle = {The Spin Verification System, Proceedings of a {DIMACS} Workshop, + New Brunswick, New Jersey, USA, August, 1996}, + pages = {23--31}, + year = {1996}, + crossref = {DBLP:conf/dimacs/dimacs32}, + url = {https://doi.org/10.1090/dimacs/032/03}, + doi = {10.1090/dimacs/032/03}, + timestamp = {Tue, 16 Jul 2019 16:47:56 +0200}, + biburl = {https://dblp.org/rec/bib/conf/dimacs/HolzmannPY96}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@proceedings{DBLP:conf/dimacs/dimacs32, + editor = {Jean{-}Charles Gr{\'{e}}goire and + Gerard J. Holzmann and + Doron A. Peled}, + title = {The Spin Verification System, Proceedings of a {DIMACS} Workshop, + New Brunswick, New Jersey, USA, August, 1996}, + series = {{DIMACS} Series in Discrete Mathematics and Theoretical Computer Science}, + volume = {32}, + publisher = {{DIMACS/AMS}}, + year = {1997}, + url = {https://doi.org/10.1090/dimacs/032}, + doi = {10.1090/dimacs/032}, + isbn = {978-0-8218-0680-7}, + timestamp = {Tue, 16 Jul 2019 16:47:56 +0200}, + biburl = {https://dblp.org/rec/bib/conf/dimacs/dimacs32}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{FernandezMJJ92, + author = {Jean{-}Claude Fernandez and + Laurent Mounier and + Claude Jard and + Thierry J{\'{e}}ron}, + title = {On-the-fly Verification of Finite Transition Systems}, + journal = {Formal Methods in System Design}, + volume = {1}, + number = {2/3}, + pages = {251--273}, + year = {1992}, + url = {https://doi.org/10.1007/BF00121127}, + doi = {10.1007/BF00121127}, + timestamp = {Mon, 16 Sep 2019 14:47:14 +0200}, + biburl = {https://dblp.org/rec/bib/journals/fmsd/FernandezMJJ92}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{Peled96, + author = {Doron A. Peled}, + title = {Combining Partial Order Reductions with On-the-Fly Model-Checking}, + journal = {Formal Methods in System Design}, + volume = {8}, + number = {1}, + pages = {39--64}, + year = {1996}, + url = {https://doi.org/10.1007/BF00121262}, + doi = {10.1007/BF00121262}, + timestamp = {Sat, 27 May 2017 14:24:05 +0200}, + biburl = {https://dblp.org/rec/bib/journals/fmsd/Peled96}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{ClarkeGH97, + author = {Edmund M. Clarke and + Orna Grumberg and + Kiyoharu Hamaguchi}, + title = {Another Look at {LTL} Model Checking}, + journal = {Formal Methods in System Design}, + volume = {10}, + number = {1}, + pages = {47--71}, + year = {1997}, + url = {https://doi.org/10.1023/A:1008615614281}, + doi = {10.1023/A:1008615614281}, + timestamp = {Sat, 27 May 2017 14:24:04 +0200}, + biburl = {https://dblp.org/rec/bib/journals/fmsd/ClarkeGH97}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{BabarBDM10, + author = {Junaid Babar and + Marco Beccuti and + Susanna Donatelli and + Andrew S. Miner}, + title = {GreatSPN Enhanced with Decision Diagram Data Structures}, + booktitle = {Applications and Theory of Petri Nets, 31st International Conference, + {PETRI} {NETS} 2010, Braga, Portugal, June 21-25, 2010. Proceedings}, + pages = {308--317}, + year = {2010}, + crossref = {DBLP:conf/apn/2010}, + url = {https://doi.org/10.1007/978-3-642-13675-7\_19}, + doi = {10.1007/978-3-642-13675-7\_19}, + timestamp = {Tue, 14 May 2019 10:00:45 +0200}, + biburl = {https://dblp.org/rec/bib/conf/apn/BabarBDM10}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@proceedings{DBLP:conf/apn/2010, + editor = {Johan Lilius and + Wojciech Penczek}, + title = {Applications and Theory of Petri Nets, 31st International Conference, + {PETRI} {NETS} 2010, Braga, Portugal, June 21-25, 2010. Proceedings}, + series = {Lecture Notes in Computer Science}, + volume = {6128}, + publisher = {Springer}, + year = {2010}, + url = {https://doi.org/10.1007/978-3-642-13675-7}, + doi = {10.1007/978-3-642-13675-7}, + isbn = {978-3-642-13674-0}, + timestamp = {Tue, 14 May 2019 10:00:45 +0200}, + biburl = {https://dblp.org/rec/bib/conf/apn/2010}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{MDD, + author = {Kam, Timothy and Villa, Tiziano and Brayton, R.K.}, + year = {1998}, + month = {01}, + pages = {}, + title = {Multi-valued decision diagrams: Theory and applications," Multiple-Valued Logic}, + volume = {4}, + journal = {Multiple-Valued Logic} +} + +@inproceedings{Clarke08, + author = {Edmund M. Clarke}, + title = {The Birth of Model Checking}, + booktitle = {25 Years of Model Checking - History, Achievements, Perspectives}, + pages = {1--26}, + year = {2008}, + crossref = {DBLP:conf/spin/5000}, + url = {https://doi.org/10.1007/978-3-540-69850-0\_1}, + doi = {10.1007/978-3-540-69850-0\_1}, + timestamp = {Tue, 14 May 2019 10:00:36 +0200}, + biburl = {https://dblp.org/rec/bib/conf/spin/Clarke08}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@proceedings{DBLP:conf/spin/5000, + editor = {Orna Grumberg and + Helmut Veith}, + title = {25 Years of Model Checking - History, Achievements, Perspectives}, + series = {Lecture Notes in Computer Science}, + volume = {5000}, + publisher = {Springer}, + year = {2008}, + url = {https://doi.org/10.1007/978-3-540-69850-0}, + doi = {10.1007/978-3-540-69850-0}, + isbn = {978-3-540-69849-4}, + timestamp = {Tue, 14 May 2019 10:00:36 +0200}, + biburl = {https://dblp.org/rec/bib/conf/spin/5000}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{KantLMPBD15, + author = {Gijs Kant and + Alfons Laarman and + Jeroen Meijer and + Jaco van de Pol and + Stefan Blom and + Tom van Dijk}, + title = {LTSmin: High-Performance Language-Independent Model Checking}, + booktitle = {Tools and Algorithms for the Construction and Analysis of Systems + - 21st International Conference, {TACAS} 2015, Held as Part of the + European Joint Conferences on Theory and Practice of Software, {ETAPS} + 2015, London, UK, April 11-18, 2015. Proceedings}, + pages = {692--707}, + year = {2015}, + crossref = {DBLP:conf/tacas/2015}, + url = {https://doi.org/10.1007/978-3-662-46681-0\_61}, + doi = {10.1007/978-3-662-46681-0\_61}, + timestamp = {Tue, 20 Aug 2019 15:27:24 +0200}, + biburl = {https://dblp.org/rec/bib/conf/tacas/KantLMPBD15}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@proceedings{DBLP:conf/tacas/2015, + editor = {Christel Baier and + Cesare Tinelli}, + title = {Tools and Algorithms for the Construction and Analysis of Systems + - 21st International Conference, {TACAS} 2015, Held as Part of the + European Joint Conferences on Theory and Practice of Software, {ETAPS} + 2015, London, UK, April 11-18, 2015. Proceedings}, + series = {Lecture Notes in Computer Science}, + volume = {9035}, + publisher = {Springer}, + year = {2015}, + url = {https://doi.org/10.1007/978-3-662-46681-0}, + doi = {10.1007/978-3-662-46681-0}, + isbn = {978-3-662-46680-3}, + timestamp = {Tue, 14 May 2019 10:00:53 +0200}, + biburl = {https://dblp.org/rec/bib/conf/tacas/2015}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{DijkP17, + author = {Tom van Dijk and + Jaco van de Pol}, + title = {Sylvan: multi-core framework for decision diagrams}, + journal = {{STTT}}, + volume = {19}, + number = {6}, + pages = {675--696}, + year = {2017}, + url = {https://doi.org/10.1007/s10009-016-0433-2}, + doi = {10.1007/s10009-016-0433-2}, + timestamp = {Sun, 02 Jun 2019 21:00:20 +0200}, + biburl = {https://dblp.org/rec/bib/journals/sttt/DijkP17}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{BabarM10, + author = {Junaid Babar and + Andrew S. Miner}, + title = {Meddly: Multi-terminal and Edge-Valued Decision Diagram LibrarY}, + booktitle = {{QEST} 2010, Seventh International Conference on the Quantitative + Evaluation of Systems, Williamsburg, Virginia, USA, 15-18 September + 2010}, + pages = {195--196}, + year = {2010}, + crossref = {DBLP:conf/qest/2010}, + url = {https://doi.org/10.1109/QEST.2010.34}, + doi = {10.1109/QEST.2010.34}, + timestamp = {Wed, 16 Oct 2019 14:14:56 +0200}, + biburl = {https://dblp.org/rec/bib/conf/qest/BabarM10}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@proceedings{DBLP:conf/qest/2010, + title = {{QEST} 2010, Seventh International Conference on the Quantitative + Evaluation of Systems, Williamsburg, Virginia, USA, 15-18 September + 2010}, + publisher = {{IEEE} Computer Society}, + year = {2010}, + url = {https://ieeexplore.ieee.org/xpl/conhome/5599994/proceeding}, + isbn = {978-0-7695-4188-4}, + timestamp = {Wed, 16 Oct 2019 14:14:56 +0200}, + biburl = {https://dblp.org/rec/bib/conf/qest/2010}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{CimattiCGGPRST02, + author = {Alessandro Cimatti and + Edmund M. Clarke and + Enrico Giunchiglia and + Fausto Giunchiglia and + Marco Pistore and + Marco Roveri and + Roberto Sebastiani and + Armando Tacchella}, + title = {NuSMV 2: An OpenSource Tool for Symbolic Model Checking}, + booktitle = {Computer Aided Verification, 14th International Conference, {CAV} + 2002,Copenhagen, Denmark, July 27-31, 2002, Proceedings}, + pages = {359--364}, + year = {2002}, + crossref = {DBLP:conf/cav/2002}, + url = {https://doi.org/10.1007/3-540-45657-0\_29}, + doi = {10.1007/3-540-45657-0\_29}, + timestamp = {Sun, 02 Jun 2019 21:10:36 +0200}, + biburl = {https://dblp.org/rec/bib/conf/cav/CimattiCGGPRST02}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@proceedings{DBLP:conf/cav/2002, + editor = {Ed Brinksma and + Kim Guldstrand Larsen}, + title = {Computer Aided Verification, 14th International Conference, {CAV} + 2002,Copenhagen, Denmark, July 27-31, 2002, Proceedings}, + series = {Lecture Notes in Computer Science}, + volume = {2404}, + publisher = {Springer}, + year = {2002}, + url = {https://doi.org/10.1007/3-540-45657-0}, + doi = {10.1007/3-540-45657-0}, + isbn = {3-540-43997-8}, + timestamp = {Tue, 14 May 2019 10:00:43 +0200}, + biburl = {https://dblp.org/rec/bib/conf/cav/2002}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{BiereCCZ99, + author = {Armin Biere and + Alessandro Cimatti and + Edmund M. Clarke and + Yunshan Zhu}, + title = {Symbolic Model Checking without BDDs}, + booktitle = {Tools and Algorithms for Construction and Analysis of Systems, 5th + International Conference, {TACAS} '99, Held as Part of the European + Joint Conferences on the Theory and Practice of Software, ETAPS'99, + Amsterdam, The Netherlands, March 22-28, 1999, Proceedings}, + pages = {193--207}, + year = {1999}, + crossref = {DBLP:conf/tacas/1999}, + url = {https://doi.org/10.1007/3-540-49059-0\_14}, + doi = {10.1007/3-540-49059-0\_14}, + timestamp = {Sun, 02 Jun 2019 21:19:27 +0200}, + biburl = {https://dblp.org/rec/bib/conf/tacas/BiereCCZ99}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@proceedings{DBLP:conf/tacas/1999, + editor = {Rance Cleaveland}, + title = {Tools and Algorithms for Construction and Analysis of Systems, 5th + International Conference, {TACAS} '99, Held as Part of the European + Joint Conferences on the Theory and Practice of Software, ETAPS'99, + Amsterdam, The Netherlands, March 22-28, 1999, Proceedings}, + series = {Lecture Notes in Computer Science}, + volume = {1579}, + publisher = {Springer}, + year = {1999}, + url = {https://doi.org/10.1007/3-540-49059-0}, + doi = {10.1007/3-540-49059-0}, + isbn = {3-540-65703-7}, + timestamp = {Tue, 14 May 2019 10:00:53 +0200}, + biburl = {https://dblp.org/rec/bib/conf/tacas/1999}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{AmparoreDBGM17, + author = {Elvio Gilberto Amparore and + Susanna Donatelli and + Marco Beccuti and + Giulio Garbi and + Andrew S. Miner}, + title = {Decision Diagrams for Petri Nets: Which Variable Ordering?}, + booktitle = {Proceedings of the International Workshop on Petri Nets and Software + Engineering (PNSE'17), co-located with the38th International Conference + on Application and Theory of Petri Nets and Concurrency Petri Nets + 2017 and the 17th International Conference on Application of Concurrency + to System Design {ACSD} 2017, Zaragoza, Spain, June 25-30, 2017}, + pages = {31--50}, + year = {2017}, + crossref = {DBLP:conf/apn/2017pnse}, + url = {http://ceur-ws.org/Vol-1846/paper3.pdf}, + timestamp = {Tue, 28 May 2019 16:23:32 +0200}, + biburl = {https://dblp.org/rec/bib/conf/apn/AmparoreDBGM17}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@proceedings{DBLP:conf/apn/2017pnse, + editor = {Daniel Moldt and + Lawrence Cabac and + Heiko R{\"{o}}lke}, + title = {Proceedings of the International Workshop on Petri Nets and Software + Engineering (PNSE'17), co-located with the38th International Conference + on Application and Theory of Petri Nets and Concurrency Petri Nets + 2017 and the 17th International Conference on Application of Concurrency + to System Design {ACSD} 2017, Zaragoza, Spain, June 25-30, 2017}, + series = {{CEUR} Workshop Proceedings}, + volume = {1846}, + publisher = {CEUR-WS.org}, + year = {2017}, + url = {http://ceur-ws.org/Vol-1846}, + urn = {urn:nbn:de:0074-1846-1}, + timestamp = {Tue, 28 May 2019 16:23:32 +0200}, + biburl = {https://dblp.org/rec/bib/conf/apn/2017pnse}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{BolligW96, + author = {Beate Bollig and + Ingo Wegener}, + title = {Improving the Variable Ordering of OBDDs Is NP-Complete}, + journal = {{IEEE} Trans. Computers}, + volume = {45}, + number = {9}, + pages = {993--1002}, + year = {1996}, + url = {https://doi.org/10.1109/12.537122}, + doi = {10.1109/12.537122}, + timestamp = {Wed, 14 Nov 2018 10:48:34 +0100}, + biburl = {https://dblp.org/rec/bib/journals/tc/BolligW96}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{Bryant86, + author = {Randal E. Bryant}, + title = {Graph-Based Algorithms for Boolean Function Manipulation}, + journal = {{IEEE} Trans. Computers}, + volume = {35}, + number = {8}, + pages = {677--691}, + year = {1986}, + url = {https://doi.org/10.1109/TC.1986.1676819}, + doi = {10.1109/TC.1986.1676819}, + timestamp = {Wed, 14 Nov 2018 10:48:32 +0100}, + biburl = {https://dblp.org/rec/bib/journals/tc/Bryant86}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{Vardi95, + author = {Moshe Y. Vardi}, + title = {An Automata-Theoretic Approach to Linear Temporal Logic}, + booktitle = {Logics for Concurrency - Structure versus Automata (8th Banff Higher + Order Workshop, Banff, Canada, August 27 - September 3, 1995, Proceedings)}, + pages = {238--266}, + year = {1995}, + crossref = {DBLP:conf/banff/1995}, + url = {https://doi.org/10.1007/3-540-60915-6\_6}, + doi = {10.1007/3-540-60915-6\_6}, + timestamp = {Sun, 02 Jun 2019 21:10:52 +0200}, + biburl = {https://dblp.org/rec/bib/conf/banff/Vardi95}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@proceedings{DBLP:conf/banff/1995, + editor = {Faron Moller and + Graham M. Birtwistle}, + title = {Logics for Concurrency - Structure versus Automata (8th Banff Higher + Order Workshop, Banff, Canada, August 27 - September 3, 1995, Proceedings)}, + series = {Lecture Notes in Computer Science}, + volume = {1043}, + publisher = {Springer}, + year = {1996}, + url = {https://doi.org/10.1007/3-540-60915-6}, + doi = {10.1007/3-540-60915-6}, + isbn = {3-540-60915-6}, + timestamp = {Sun, 02 Jun 2019 21:10:52 +0200}, + biburl = {https://dblp.org/rec/bib/conf/banff/1995}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{VardiW94, + author = {Moshe Y. Vardi and + Pierre Wolper}, + title = {Reasoning About Infinite Computations}, + journal = {Inf. Comput.}, + volume = {115}, + number = {1}, + pages = {1--37}, + year = {1994}, + url = {https://doi.org/10.1006/inco.1994.1092}, + doi = {10.1006/inco.1994.1092}, + timestamp = {Wed, 14 Nov 2018 10:35:07 +0100}, + biburl = {https://dblp.org/rec/bib/journals/iandc/VardiW94}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{ClarkeES86, + author = {Edmund M. Clarke and + E. Allen Emerson and + A. Prasad Sistla}, + title = {Automatic Verification of Finite-State Concurrent Systems Using Temporal + Logic Specifications}, + journal = {{ACM} Trans. Program. Lang. Syst.}, + volume = {8}, + number = {2}, + pages = {244--263}, + year = {1986}, + url = {https://doi.org/10.1145/5397.5399}, + doi = {10.1145/5397.5399}, + timestamp = {Wed, 14 Nov 2018 10:30:40 +0100}, + biburl = {https://dblp.org/rec/bib/journals/toplas/ClarkeES86}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} \ No newline at end of file diff --git a/tesi/galla/tesi.blg b/tesi/galla/tesi.blg new file mode 100644 index 0000000..ff52ee7 --- /dev/null +++ b/tesi/galla/tesi.blg @@ -0,0 +1,46 @@ +This is BibTeX, Version 0.99d (TeX Live 2019 Gentoo Linux) +Capacity: max_strings=100000, hash_size=100000, hash_prime=85009 +The top-level auxiliary file: tesi.aux +The style file: /usr/share/texmf-dist/bibtex/bst/base/acm.bst +Database file #1: tesi.bib +You've used 26 entries, + 2253 wiz_defined-function locations, + 761 strings with 10388 characters, +and the built_in function-call counts, 10476 in all, are: += -- 1027 +> -- 463 +< -- 0 ++ -- 184 +- -- 153 +* -- 858 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100644 index 0000000..f92fb38 --- /dev/null +++ b/tesi/galla/tesi.org @@ -0,0 +1,467 @@ +#+TITLE: An automata-based implementation of a symbolic CTL* model checker +#+AUTHOR: Francesco Galla' +#+EMAIL: galla@di.unito.it +#+DATE: + +#+LANGUAGE: en + +#+LaTeX_CLASS: article +#+LaTeX_HEADER: \usepackage[utf8]{inputenc} +#+LaTeX_HEADER: \usepackage{algorithm} +#+LaTeX_HEADER: \usepackage{algpseudocode} +#+LaTeX_HEADER: \usepackage{amsmath,amssymb,amsthm} +#+Latex_HEADER: \newtheorem{definition}{Definition} +#+LaTeX_HEADER: \usepackage{graphicx} +#+LaTeX_HEADER: \usepackage{listings} +#+LaTeX_HEADER: \usepackage{color} + +#+EXPORT_SELECT_TAGS: export +#+EXPORT_EXCLUDE_TAGS: noexport +#+OPTIONS: H:2 toc:nil \n:nil @:t ::t |:t ^:{} _:{} *:t TeX:t LaTeX:t +#+STARTUP: showall + +\begin{abstract} + +This dissertation presents the implementation of a symbolic CTL* model +checking algorithm based on multi-valued decision diagrams (MDDs). +Given a Petri Net model and a CTL* proposition, the algorithm is capable +of identifying LTL sub-formulae, translate them to Büchi automata and +compute the synchronized product of each LTL formula with the model. +MDDs are used to encode the Petri Net and such composition, provably +lowering both system memory and time required to manipulate its graph +of reachable states with respect to explicit model checking tecniques. +By combining the sets of satisfying states for each LTL sub-formula +according to the temporal quantifiers preceding them, the algorithm is +capable of producing the boolean satisfaction result of the CTL* formula +and a counterexample or witness run describing such outcome. +Timed test runs executed againts a large set of models and specifications of +LTL, CTL and CTL* temporal logics show competitive performance results +with respect to other tools which process CTL* by translating each +formula to $\mu$-calculus. This algorithm has been implemented as one +of the free and open source programs composing the GreatSPN framework +for formal verification of systems. + +\end{abstract} + +# Model checking is a formal verification technique intended to analyze +# properties of system designs. Model checking is based upon a formal +# model describing a system and a specification provided using a +# temporal logic formula such as LTL, CTL or CTL*. +# The algorithmic analysis of the Kripke structure representing the +# composition of the model and the specification requires the +# manipulation of the graph of its reachable states, which can be +# arbitrarely large in size depending on model characteristics and +# formula provided. Frequently, explicit enumeration of reachable states +# of a complex model requires a large amount of memory and time. +# Tecniques based on symbolic representation of such reachability graphs +# exploit the abstractions provided by decision diagrams, provably +# allowing for a sensible reduction in time and memory consumption while +# ensuring equivalent results with respect to explicit tecniques. CTL* +# is a temporal logic defined as a superset of Linear Temporal Logic +# (LTL) and Computational Tree Logic (CTL). CTL* is motivated by the +# incomparable expressiveness of LTL and CTL, which historically caused +# a proliferation of model checking tools geared towards the former or +# the latter logic, each one presenting its own limitations. The +# theoretical literature formalizing symbolic CTL* model checking +# algorithms describes two different approaches. One exploits the +# translation of CTL* formulae to $\mu$-calculus and is currently used +# by all model checking tools we were able to find and inspect. The +# other identifies LTL sub-formulae contained into a given CTL* +# proposition, obtains the sets of states satisfying such formulae using +# a LTL model checkers and combines them according to the temporal +# quantifier preceding each sub-formula to obtain a satisfaction result +# and a counter-example or witness run on the given model. This +# dissertation describes the implementation of a symbolic CTL* model +# checker which uses such LTL-based tecnique at its core. Competitive +# performance results were obtained by testing this algorithm against +# other research tools which use the $\mu$-calculus tecnique. This +# algorithm has been implemented as one of the programs composing the +# GreatSPN framework for formal verification of systems based on Petri Nets. + + +* Introduction + +** Model Checking + +Model checking is a formal verification technique intended to analyze properties +of system designs. Given a formal model and a specification, the objective of +model checking is to decide whether the behavior of the model satisfies the +specification or not. The model is usually represented as a Kripke structure or +by a high-level formalism that can be transformed into a Kripke structure. +Examples of these formalisms are Petri Nets and Process algebra. + +The specification is provided using a temporal logic expression, that is, a +formula that expresses a temporal and logical statement. Temporal logics are +modal logics geared towards the description of the temporal ordering of events. +It is important to clarify that these logics do not consider precise timing +requirements of activities or events, but reason about their +/abstract temporal order/. For this reason, they are particularly useful when +applied to concurrent systems in which all components proceed in a +lock-step fashion over a discrete time domain. The system behavior is assumed to +be observable at integral time points and each time point identifies a snapshot +of all variables of the system, called /state/. + +Two brands of temporal logics have been proposed over the years for specifying +the properties of reactive systems. Linear Temporal Logic \cite{Pnueli77} is +based on /linear time/, therefore considering every moment in time as having a +unique possible future. Computational Tree Logic \cite{ClarkeE81} is defined +upon /branching time/: it pictures the structure of time as a tree, +allowing each moment in time to split into different possible futures. +From now on we will refer to these two logics using their well-known acronyms +LTL and CTL respectively. + +# IMAGE: ltl vs ctl + +The difference between LTL and CTL is rooted in their satisfaction relations, +which are conceptually different. LTL is said to be path-based, since a +system /S/ satisfies a LTL formula \phi if for all initial paths of /S/, +paths starting in an intial state $s_{\textit{0}}$ satisfy \phi. +Conversely, CTL is said to be state-based, since a system /S/ satisfies +a CTL formula \phi if and only if \phi holds in all initial states of /S/. + +Furthermore, the expressiveness of LTL and CTL temporal logics is incomparable +\cite{Lamport80}. Conversely, CTL is particularly useful to express the +/possibility/ of existence of a specific path of execution of a model, that +is, the occurrence of an event happening on one branch but not necessarily all +of them. This concept cannot be expressed using a formalism based on linear time +such as LTL, which describes executions of a system, not the way those +executions are organized in a branching tree. On the contrary, CTL cannot +express situations in which the same behavior may occur on distinct branches at +distinct times, while the ability of LTL to describe individual paths is +more convenient in this case. In practice, the LTL formula *FG*\phi is not +expressible in CTL, while the formula *AFAG*\phi is not expressible in LTL. +Given the shortcomings of both these temporal logics, a superset of LTL and CTL +called CTL* \cite{EmersonH86} has been introduced. \\ + +** A brief history of LTL model checking + +Model checking LTL properties comes down to checking language emptyness of the +syncronized product between the Kripke structure representing the model and a +formalism which can represent a LTL formula while being translatable to a +Kripke structure, namely a Büchi automaton. This /automata-theoretic approach/ +\cite{Vardi95} treats the synchronized product as a transition system +\cite{Keller76} whose state graph can be analyzed using tecniques +classified in two main categories: + +- /Explicit/ methods process the state graph of the synchronized product using + graph traversal algorithms. +- /Symbolic/ methods represent the state graph using /decision diagrams/ and + usually apply fixed point algorithms to the set of states to find the strongly + connected components (SCCs) of the transition system. + +Explicit methods are based on graph traversal algorithms but are often limited +by the complexity of the LTL model checking problem, which is constrained by the +size of the state space of the model, the size of the underlying automaton used +to represent the formula and the combined size of the two Kripke structures in +a transition system. More specifically, the model checking problem for LTL is +known to be PSPACE-complete \cite{Sistlac85}. +Historically, the first LTL model checkers were explicit: a notable example is +SPIN \cite{Holzmann97}, which takes advantage of an optimized version of Tarjan +DFS algorithm for finding strongly connected components in a graph, +called /Nested Depth First Search/ \cite{HolzmannPy96}. + +In practice, model checkers applied to complex, real-world sistems have to +face the /state space explosion/ problem: the exponential growth in +the number of variables of the state graph dimension. Given that, in general, +a system with /n/ variables over a domain of /k/ possible values requires +at least $n^{\textit{k}}$ states in the reachability set, it is +understandable how even a simple model might necessitate a large reachability +graph. Furthermore, dealing with real-valued variables, which have infinite +possible assignments, results in a reachability graph with infinitely many +states. + +This problem has encouraged the development of various tecniques which have +proven to be successful in mitigating the state explosion. Explicit model +checkers have introduced /on-the-fly/ state-space construction +to avoid storing the whole state graph. The most basic /on-the-fly/ algorithm +\cite{FernandezMJJ92} stores states which have already been visited in memory +and is therefore able to check for cycles in the reachability graph while +generating it through DFS. SPIN uses /on-the-fly/ state graph construction +combined with /partial order reduction/ \cite{Peled96}, a tecnique which reduces +the size of the reachability graph by exploiting commutativity of concurrently +executed transitions which result in the same state. + +** The origin of symbolic model checking + +Efforts towards state space minimization have been particularly successful in +developing clever representation of the state graph. /Symbolic/ model checking +represent the system model and the LTL formula using set of states and set +of transitions. These sets can be represented as solutions to +logical equations, using decision diagrams to represent this +state space implicitly. +Since syntactically small equations can represent large set of states, +this tecnique ultimately avoids building the state graph explicitly, +thus saving space in memory. Above all, Ordered Binary Decision Diagrams (OBDDs) +provide a canonical form for boolean formulae which can be substantially more +compact than conjunctive or disjuntive normal form and efficient algorithms have +been implemented for manipulating them. McMillan was the first to introduce +the use of OBDDs to represent the state space of a model, developing a CTL +model checking tool called SMV \cite{SymbMC}. +Symbolic model checking is considered to be one of the biggest breakthrough in +the history of model checking for its impact on the state explosion problem +\cite{Clarke08}. + +Symbolic model checking was initially applied to CTL because of the +significantly lower complexity of the model checking problem with +respect to LTL: CTL model checking is known to be P-Complete and its +time complexity is bilinear in the size of the model and of the +formula \cite{ClarkeES86}. After the introduction of SMV, further research work +increased the capabilities of decision diagrams. By introducing +Multi-valued decision diagrams (MDDs) , tools were able to represent +integral and real-valued functions, thus enhancing the applications of +symbolic strategies to formal verification. In recent years, the +LTSmin tool \cite{KantLMPBD15} developed by the University of Twente +employs the SYLVAN multi-core MDDs library \cite{DijkP17} to speed up +symbolic analysis algorithms for CTL model checking. A different +solution was adopted by an extended version of SMV, NuSMV +\cite{CimattiCGGPRST02}, which mantained the specification language of +McMillan's tool while improving it by introducing LTL model checking +and +Sat-based Bounded model checking \cite{BiereCCZ99}, which exploits propositional +satisfiability without using BDDs to represent the state graph. +This approach was chosen because working with decision diagrams does not +always guarantee an improvement over explicit model checking +tecniques due to the often time-consuming procedure of selecting a variable +ordering for all variables in the system, which is a known NP-complete problem +\cite{BolligW96}. + +Until the present day, our GreatSPN framework used multi-valued, multi-terminal +decision diagrams (MTMDDs) provided by the Meddly library \cite{BabarM10} to +perform CTL model checking on Petri Nets \cite{BabarBDM10}. Meddly is possibly +the only open-source library to implement MTMDDs, Edge-valued MDDs (EVMDDs) +while providing state-of-the-art algorithms to manipulate them. +To determine the optimal variable ordering for the MDDs used to represet the +state graph, GreatSPN uses a set of algorithms based on different heuristics +which are run during the state space generation procedure \cite{AmparoreDBGM17}. +As we are going to discuss later in this dissertation, GreatSPN is now capable +of CTL* model checking by reducing symbolic LTL model checking to CTL model +checking with fairness constraints, as demonstrated in a notorious article +\cite{ClarkeGH97} by Clarke et al. + +* Background + +** Linear Temporal Logic + +LTL is a propositional temporal logic with linear time model, meaning that it +considers a single realized future behavior of a system, that is, a single +path in a Kripke structure. + +#+ATTR_LATEX: :environment definition +#+BEGIN_definition +/Syntax of LTL/. The formal syntax of LTL is given by the following grammar in +Backus-Naur form (BNF), where /a/ \in /AP/ is an atomic proposition. + +#+BEGIN_center +/\phi ::= true | a | \not\phi | \phi \wedge \phi | *X*\phi | \phi *U* \phi/ +#+END_center + +#+END_definition + +Using boolean connectors such as \not and \wedge allows LTL to be treated as +a propositional logic. Other boolean connectives such as disjunction \vee, +implication \rightarrow, equivalence \leftrightarrow and the exclusive or (xor) +operator \oplus can be derived as for any other propositional logic. +This LTL grammar is defined using two basic temporal modalities: *X* (next) and +*U* (until). Using those, we can derive two essential temporal modalities *F* +(eventually) and *G* (always), as follows: + +#+BEGIN_center +*F*\phi = /true/\textbf{U}\phi \\ +*G*\phi = \not\textbf{F}\not\phi +#+END_CENTER + +We now present a list of the temporal modalities which will be used at a later +time in this dissertation. + +- *G*\phi: "always" (now and forever in the future \phi is true) +- *F*\phi: "eventually" (eventually in the future \phi is true) +- *X*\phi: "next" (in the next time step \phi is true) +- \psi\textbf{U}\phi: "until" (\psi is true until \phi is true) + +By combining the aforementioned temporal operators we obtain other, more complex +modalities. A typical example is the specification which requires a property to +be true /infinitely often/, *GF*\phi. + + +\paragraph{LTL Semantics} +LTL semantics is defined for /infinite words/ \sigma over the alphabet +2\textsuperscript{AP}. The satisfiability rules are shown below: + +- \(\sigma \vDash true\) +- \(\sigma \vDash a\) iff \(a \in A_{0}\) +- \(\sigma \vDash \phi_{1} \wedge \phi_{2}\) iff \(\sigma \vDash \phi_{1}\) and \(\sigma \vDash \phi_{2}\) +- \(\sigma \vDash \neg\phi\) iff \(\neg (\sigma \vDash \phi)\) +- \(\sigma \vDash \textbf{X}\phi\) iff \(\sigma[1...] \vDash \phi\) +- \(\sigma \vDash \phi_{1}\textbf{U}\phi_{2}\) iff \(\exists j \geq 0, \sigma[j...] \vDash \phi_{2}\) and \(\sigma[i...] \vDash \phi_{1}\) for all \(0 \leq i < j\) + +A LTL formula \phi is said to be /valid/ with regard +to a Kripke structure /M/ if it holds for all paths of /M/. It is /satisfiable/ +if it holds for some path in /M/. + +** CTL* + +We briefly introduced CTL* while dealing with the shortcomings of LTL and CTL. +CTL* is a branching temporal logic which extends CTL following a proposal by +Emerson and Halpern. Being based on the concept of branching time, CTL* is able +to represent the possibility of existence of a determinate behavior in a tree of +execution, using CTL path quantifiers *E* (for some path) and *A* (for all +paths) to specify whether the required behavior must be verified for some +execution of our system or all possible ones. + +CTL* allows path quantifiers to be arbitrarely nested with linear temporal +operators *G*, *F*, *X* and *U*. In contrast, CTL only supports linear +temporal operators if they are immediately preceded by a path quantifier. +In a similar fashion as CTL, the syntax of CTL* distinguishes between +/state/ and /path/ formulae. CTL* path formulae are defined as LTL formulae, +whith the only difference that here state formulae can be used as atoms. + +#+BEGIN_definition +/Syntax of CTL*/. The formal syntax of /CTL*/ is made of state formulae \Phi and +path formulae \phi. The syntax of /CTL*/ state formulae \Phi is defined over the +set /AP/ of atomic propositions: + +#+BEGIN_center +/\Phi ::= true | a | \not\phi | \phi \wedge \phi | *E*\phi/ +#+END_center + +The syntax of CTL* path formulae \phi is given by the following grammar, where +\Phi is a state formula: + +#+BEGIN_center +/\phi ::= \Phi | \not\phi | \phi \wedge \phi | *X*\phi | \phi *U* \phi/ +#+END_center + +#+END_definition + +As previously seen for LTL, the syntax of CTL* can be treated as any +propositional logic, therefore all boolean connectives can be derived from +\not and \wedge. The missing temporal modalities *F* and *G* descend from +*X* and *U* as it was the case for LTL, while the path quantifier *A* can be +obtained from the following equivalence: + +#+BEGIN_center +*A*\phi = \not\textbf{E}\not\phi +#+END_CENTER + +\paragraph{CTL* Semantics} +Let a \in /AP/ be an atomic proposition, $TS = (S, Act, \rightarrow, I, AP, L)$ +be a transition system without terminal states, state /s/ \in /S/, \Phi and \Psi +be CTL* state formulae and \phi, \phi\textsubscript{1} and \phi\textsubscript{2} +be CTL* path formulae. + +\paragraph{State formulae: semantics} + +- \(s \vDash a\) iff \(a \in \textit{L(s)}\) +- \(s \vDash \Phi \wedge \Psi\) iff \(s \vDash \Phi\) and \(s \vDash \Psi\) +- \(s \vDash \neg\Phi\) iff \(\neg (s \vDash \Phi)\) +- \(s \vDash \textbf{E}\phi\) iff \(\sigma \vDash \phi\) for some \(\sigma \in \textit{Paths(s)}\) + +\paragraph{Path formulae: semantics} + +- \(\sigma \vDash \Phi\) iff \(s_{0} \vDash \Phi\) +- \(\sigma \vDash \phi_{1} \wedge \phi_{2}\) iff \(\sigma \vDash \phi_{1}\) and \(\sigma \vDash \phi_{2}\) +- \(\sigma \vDash \neg\phi\) iff \(\neg (\sigma \vDash \phi)\) +- \(\sigma \vDash \textbf{X}\phi\) iff \(\sigma[1...] \vDash \phi\) +- \(\sigma \vDash \phi_{1}\textbf{U}\phi_{2}\) iff \(\exists j \geq 0, \sigma[j...] \vDash \phi_{2}\) and \(\sigma[i...] \vDash \phi_{1}\) for all \(0 \leq i < j\) + +** Decision Diagrams + +Decision diagrams are directed, acyclic graphs used to represent functions over +variables with finitely many possible assignments. They were originally +studied by Bryant \cite{Bryant86} as a representation of boolean functions +in the form of Binary Decision Diagrams (BDDs). +We focus on a generalization of BDDs called Multi-value Decision Diagrams (MDDs) +\cite{MDD}, whose variable domain can be arbitrarely large and which can be +used to represent functions of integral and real-valued variables. + +#+BEGIN_definition +/Multi-valued Decision Diagram/. A multi-valued desicion diagram, or MDD, is an +acyclic graph in which each node represents a function over variables with +finitely many possible assignments, of the form: + +#+BEGIN_center +$f : S_{K} \times ... \times S_{1} \rightarrow \{ 0, \ldots, m - 1 \}$ +#+END_center + +Each one of the sets $S_{k}$ is considered to be finite on an +arbitrarely large domain. We can write: + +#+BEGIN_center +$S_{k} = \{ 0, 1, \ldots, n_{k} - 1 \}$ +#+END_center + +#+END_definition + +An MDD is composed of two types of nodes: /terminal/ nodes and /non-terminal/ +nodes. + +- Terminal nodes are labeled with values from the set $\{0,1,\ldots,m-1\}$, + representing the constant function: + +#+BEGIN_center +$g (x_{K},\ldots,x_{1}) = a$ +#+END_center + +- Non-terminal nodes are labeled with one of the function variables + $x_{k}$ and contain $n_{k}$ arcs to other nodes. + +A non terminal node labeled with $x\textsubscript{k}$ has an outgoing arc +corresponding to value $v$ which goes to a node representing the function: + +#+BEGIN_center +$f_{x_{k}=v}(x_{K},\ldots,x_{1}) \equiv f(x_{K},\ldots,x_{k+1},v,x_{k-1},\ldots,x_{1})$ +#+END_center + +\paragraph{Reduced ordered MDDs} +In the contest of model checking, MDDs are useful to encode the state space +of a model as a boolean, integral or real-valued function. +To fit this purpose, MDDs must be in /canonical/ form, meaning that +for any given function and variable ordering, there must be exactly /one/ +representation of that function as MDD. For this to be true, we have to impose +two constraints on MDDs: that they are /ordered/ and /reduced/ (ROMDDs). + +#+BEGIN_definition +/Ordered MDDs/. An MDD is ordered if all paths through the MDD visit +non-terminal nodes accortding to the same variable ordering. +#+END_definition + +#+BEGIN_definition +/Reduced Ordered MDDs/. A reduced, ordered MDD is an ordered MDD that contains +no duplicate nodes and no redundant nodes. + +- Two nodes are *redundant* if all of its outgoing arcs point to the same node. +- Two terminal nodes are *duplicates* if they have the same label, while two + non-terminal nodes are duplicates if they have the same variable label and + the same outgoing arcs for each value. +#+END_definition + +# ESEMPI MDD, GraphViz plot di RS (modello semplice, pochi stati) + +** Automata over infinite words + +We've described how Linear Temporal Logic provides a language to describe the +temporal order of a series of events. When applied to formal verification, +these sequences of events can be interpreted as computations of the program. +A computation is a potentially infinite sequence of program states: each state +is described by a finite set of atomic propositions, which will be referred to +as a nonempty /alphabet/. Therefore a computation can be treated as an +infinite word over the alphabet of truth assignments to the atomic propositions +of a given alphabet. + +This reasoning suggests that a LTL specification can be thought of as a +description of a /language/ over some alphabet. This language is made of +infinite /words/, which represent program computations. We can exploit this +equivalence of computations and words to connect linear temporal logic to +automata theory applied on infinite words. As we are going to show, automata +over infinite words depict a suitable formalism to represent LTL specifications. +More precisely, given any propositional temporal formula, one can construct a +/finite automaton/ over infinite words that accepts precisely the computations +satisfied by the formula \cite{VardiW94}. This chapter will present an +introduction to automata theory and describe how LTL model checking employs a +particular class of automata over infinite words, called /Büchi automata/. + +# CTL* model checking + +# * Emerson-Lei & alternatives +\bibliographystyle{/usr/share/texmf-dist/bibtex/bst/base/acm} +\bibliography{tesi} diff --git a/tesi/galla/tesi.out b/tesi/galla/tesi.out new file mode 100644 index 0000000..04c5e79 --- /dev/null +++ b/tesi/galla/tesi.out @@ -0,0 +1,9 @@ +\BOOKMARK [1][-]{section.1}{Introduction}{}% 1 +\BOOKMARK [2][-]{subsection.1.1}{Model Checking}{section.1}% 2 +\BOOKMARK [2][-]{subsection.1.2}{A brief history of LTL model checking}{section.1}% 3 +\BOOKMARK [2][-]{subsection.1.3}{The origin of symbolic model checking}{section.1}% 4 +\BOOKMARK [1][-]{section.2}{Background}{}% 5 +\BOOKMARK [2][-]{subsection.2.1}{Linear Temporal Logic}{section.2}% 6 +\BOOKMARK [2][-]{subsection.2.2}{CTL*}{section.2}% 7 +\BOOKMARK [2][-]{subsection.2.3}{Decision Diagrams}{section.2}% 8 +\BOOKMARK [2][-]{subsection.2.4}{Automata over infinite words}{section.2}% 9 diff --git a/tesi/galla/tesi.pdf b/tesi/galla/tesi.pdf new file mode 100644 index 0000000000000000000000000000000000000000..abb5d801eb8e78ff2fe3d239090600e6f8e649bc GIT binary patch literal 349379 zcma&tLz^%#+6CycZQHhO+qP}nwr$(CZQHi1-szcZc3&?#tNenTJ10*_6-2~n8R=M| zNEcQ{H=tM;2^a|MjjW(}c%bNIOzq5FEC?7mSl9^uzXe4vW@+PM>O?>kB zSKq_{-$bHq>sH<0yPwsHU%jz>yny#w@LPK~D`)cNQ8l~Ba!v6J#=Eh0*#>VH%kujv zfwkQlzu(rj`jtP6PmMYzh?PpsuOtX5{$YL3=H5S5WITPvtvua9gbY4BOZ=M=H)8;Q zDm5sSCDszI0czOubd1nVHF`GN711Ndo_a}*5nH^|z3N))U-(Mz;OUHejUB(rC-SsF$9qdgl5#(z`2pfBiWOC>%FWy5PY(dnMXj| zGk6IDPMmAr18v_I@+cQGOJh8wb!1D3nz}rC8m(hBc&>+PuJ6kSM$#`*Gz*!4vSlOPqnSR2s(20 zTMpmbjjHGE+&Lo*f4~2JvC81q-1BmGtKI~M;v+K3Vm?x7kJr;8Y;Niy8Pg<-J!Lvf zqjxhhEUghC4y3$}7gD8{)IwhvhZ-(l~0)gWyo;_jPLV_{Kt7g1sIA*b^uGohBk?lpw zeVR}9E!9`)B}!AmjuKuWT+xjS0xlOPlI!v!q^@O^ zxEZ5eC{8TJ8&E*uu)N)veoH 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\end{wrapfigure} +% -- - ---- --- +% [number of narrow lines] {placement} [overhang] {width of figure} +% +% Placement is one of r, l, i, o, R, L, I, O, for right, left, +% inside, outside, (here / FLOAT). +% The figure sticks into the margin by `overhang', if given, or by the +% length \wrapoverhang, which is normally zero. +% The number of wrapped text lines is normally calculated from the height +% of the figure, but may be specified manually ("12" above). +% +% Environments similar to "wrapfigure" and "wraptable" may be easily added, +% or invoked by "\begin{wrapfloat}{float_name}" +% +% More detailed instructions are given below, following the definitions. +% Please direct any problem reports to asnd@triumf.ca + +%%%%% ----- Begin definitions ----- %%%%% + +\@ifundefined{c@WF@wrappedlines}{}{\endinput} + +\newdimen\wrapoverhang \wrapoverhang\z@ +\newdimen\WF@size +\newcount\c@WF@wrappedlines % used globally +\newbox\WF@box +\newtoks\WF@everypar +\newif\ifWF@float +\let\@@parshape\parshape +\let\WF@@everypar\everypar + +\def\wrapfloat#1{\def\@captype{#1}\@ifnextchar[\WF@wr{\WF@wr[]}} + +\def\wrapfigure{\wrapfloat{figure}} +\def\wraptable{\wrapfloat{table}} + +\def\WF@wr[#1]#2{% first two args: #1=num lines, #2=placement + \xdef\WF@wfname{wrap\@captype\space}% + \ifvoid\WF@box\else \WFclear \WF@collision \fi + \xdef\WF@place{\string`\@car#2r\@nil}% + \ifnum\lccode\WF@place=\WF@place \global\WF@floatfalse + \else \global\WF@floattrue \fi + \ifx\parshape\WF@fudgeparshape \ifWF@float\else\WF@collision\fi \else + \ifx\par\@@par \ifnum\@@parshape>\z@\WF@conflict\fi \else \WF@conflict\fi + \fi \gdef\WF@wli{#1}% + \@ifnextchar[\WF@rapt{\WF@rapt[\wrapoverhang]}} + +\def\WF@rapt[#1]#2{% final two args: #1 = overhang, #2 = width, + \gdef\WF@ovh{#1}% hold overhang for later, when \width is known + \global\setbox\WF@box\vtop\bgroup \setlength\hsize{#2}% + \ifdim\hsize>\z@ \@parboxrestore \else + \setbox\z@\hbox\bgroup \let\wf@@caption\caption \let\caption\wf@caption + \ignorespaces \fi} + +\def\wf@caption{\relax + \ifdim\hsize>\z@ \let\caption\wf@@caption \else + \unskip \egroup \hsize\wd\z@ \@parboxrestore \box\z@ \fi \caption} + +\def\endwrapfloat{% + \ifdim\hsize>\z@ \par\hrule\@width\hsize\@height\z@ % force width + \else \unskip \egroup \box\z@ \fi % or end hbox + \egroup % end the \vtop; width is known so now is "later" + \WF@floatstyhook % support float.sty + \def\width{\wd\WF@box}\setlength\wrapoverhang{\WF@ovh}% + \xdef\WF@ovh{\the\wrapoverhang}% save until wrapping + \ifdim\ht\WF@box>\topskip \ht\WF@box\z@ \fi % too much height, set flag. + \ifdim\ht\WF@box<.5\p@ % too tall (starts with \vbox) or too short + \global\setbox\WF@box\vtop{\vskip-1.4ex\unvbox\WF@box}\fi + \global\WF@size\dp\WF@box % box is guaranteed to have little height. + \global\advance\WF@size1.5\baselineskip \global\advance\WF@size\tw@\intextsep + \aftergroup\WF@startfloating % even when not really floating! + \ifWF@float\else \ifhmode + {\unskip \parfillskip\z@skip \par \vskip-\parskip}\aftergroup\noindent + \fi\fi \global\@ignoretrue} + +\let\endwrapfigure\endwrapfloat +\let\endwraptable\endwrapfloat + +% Subvert \everypar to float fig and do wrapping. Also for non-float. +\def\WF@startfloating{% + \WF@everypar\expandafter{\the\everypar}\let\everypar\WF@everypar + \WF@@everypar{\ifvoid\WF@box\else\WF@floathand\fi \the\everypar + \WF@wraphand +}} + +\def\WF@floathand{% +\ifx\parshape\WF@fudgeparshape \WF@fltmes\else + \ifx\par\@@par\ifnum\@@parshape=\z@\ifdim\hangindent=\z@ + \setbox\z@\lastbox \begingroup + \@@par \WF@@everypar{}\WF@putfigmaybe + \endgroup % start wrapping + \ifvoid\z@\else\box\z@\fi % replace indentation + \else\WF@fltmes\fi\else\WF@fltmes\fi\else\WF@fltmes\fi\fi} + +% Put fig here if it fits or if it can't float +\def\WF@putfigmaybe{% +\ifinner + \vskip-\parskip \global\WF@floatfalse + \let\pagetotal\maxdimen % kludge flag for "not top of page" +\else % outer page + \@tempdima\pagedepth % save page depth + {\advance\parskip\@tempdima\vskip-\parskip}% back up to baseline + \penalty\interlinepenalty % update pg. parameters + \@tempdimb\pagegoal \advance\@tempdimb-\pagetotal % room left on page + \ifdim\@tempdimb<\z@ % \WF@info{Page overfull already;}% + \global\WF@floatfalse + \ifdim-\@tempdimb>\pageshrink \else \pagebreak \fi + \else + \ifdim\WF@size>\@tempdimb +% \WF@info{Size \the\WF@size\space does not fit in \the\@tempdimb}% + \ifWF@float \dimen@.5\baselineskip \else \dimen@ 2\baselineskip\fi + \ifdim\pagestretch>\dimen@ \dimen@\pagestretch \fi + \ifdim\pagefilstretch>\z@ \dimen@\@tempdimb \fi + \ifdim\pagefillstretch>\z@ \dimen@\@tempdimb \fi + \advance\dimen@.5\baselineskip + \ifdim\dimen@>\@tempdimb % \WF@info{Page nearly full; can stretch}% + \global\WF@floatfalse \pagebreak + \fi + \else % \WF@info{Fits in \the\@tempdimb;}% + \global\WF@floatfalse + \fi\fi + \vskip\@tempdima\relax % (return erased page depth) +\fi +\noindent +\ifWF@float + \WF@fltmes +\else % putting here; + \WF@info{Put \WF@wfname here:}% + {\ifodd\if@twoside\c@page\else\@ne\fi % assign l/r to i/o placement + \lccode`i`l\lccode`o`r\else \lccode`i`r\lccode`o`l\fi + \xdef\WF@place{\the\lccode\lccode\WF@place}}% twice to get only l or r + \hbox to\z@{% llap or rlap depending on {l} or {r}; calc effective width + \@tempdima\wd\WF@box \@tempdimb\WF@ovh + \advance\@tempdima-\@tempdimb \advance\@tempdima\columnsep + \@tempdimb\hsize \advance\@tempdimb-\@tempdima + \xdef\WF@adjlw{\the\@tempdima}% + \ifnum `l=\WF@place % fig on left + \hss % figure overlaps space to the left + \def\@tempa{\kern\columnsep}% position to left of the gap + \else % fig on right + \@tempdima\z@ % no left indentation + \kern\@tempdimb \kern\columnsep + \def\@tempa{\hss}% figure overlaps space to the right + \fi + \ifdim\@tempdimb<\hsize + \xdef\WF@wrapil{\the\@tempdima \the\@tempdimb}% indentation and length + \xdef\WF@adjtlm{\the\@tempdima}% + \else + \xdef\WF@wrapil{\z@ \the\hsize}% + \xdef\WF@adjlw{\z@}\xdef\WF@adjtlm{\z@}% + \fi + \ifdim\pagetotal=\z@ % \WF@info{Put \WF@wfname at top of p.\thepage}% + \global\advance\WF@size-\intextsep + \else % \WF@info{Putting \WF@wfname in middle of page}% + \setbox\WF@box\hbox{\lower\intextsep\box\WF@box}% + \fi \dp\WF@box\z@ \box\WF@box \@tempa + }% end \hbox to 0pt + \aftergroup\WF@startwrapping % after the \endgroup which immediately follows +\fi} + +\def\WF@startwrapping{% + \ifx\WF@wli\@empty + {\advance\WF@size1.1\baselineskip + \divide\WF@size\baselineskip \global\c@WF@wrappedlines\WF@size}% + \else + \setcounter{WF@wrappedlines}{\WF@wli}\global\advance\c@WF@wrappedlines\@ne + \fi + \ifnum\c@WF@wrappedlines>\@ne + \let\parshape\WF@fudgeparshape \let\WF@pspars\@empty \let\WF@@par\par + \def\@setpar##1{\def\WF@@par{##1}}\def\par{\@par}\let\@par\WF@mypar + \xdef\WF@restoretol{\tolerance\the\tolerance}\tolerance9999 + \advance\linewidth-\WF@adjlw \advance\@totalleftmargin\WF@adjtlm + \fi} + +\def\WF@wraphand{% +\ifnum\c@WF@wrappedlines<\tw@ \WF@finale +\else \begingroup % Create \parshape command: + \@tempcnta\@ne \let\WF@wrapil\relax \gdef\WF@ps{}% + \@whilenum \@tempcnta<\c@WF@wrappedlines\do{% repeated indentation, length + \xdef\WF@ps{\WF@ps\WF@wrapil}\advance\@tempcnta\@ne + }\endgroup + \ifx\WF@pspars\@empty + \@@parshape\c@WF@wrappedlines \WF@ps \WF@noil + \else % use external `parshape' values to modify my parshape + \WF@modps +\fi\fi} + +\def\WF@mypar{\relax + \WF@@par % what the rest of LaTeX expects \par to be (usually \@@par) + \ifnum\@@parshape=\z@ \let\WF@pspars\@empty \fi % reset `parshape' + \global\advance\c@WF@wrappedlines-\prevgraf \prevgraf\z@ + \ifnum\c@WF@wrappedlines<\tw@ \WF@finale \fi} + +\def\WF@modps{\begingroup + \afterassignment\@tempdimb \@tempdima\WF@pspars % a=ind, b=wid + \advance\@tempdima-\WF@adjtlm \advance\@tempdimb\WF@adjlw +% \afterassignment\dimen@\advance\@tempdima\WF@wrapil +% \advance\@tempdimb\dimen@ \advance\@tempdimb-\hsize + \let\WF@wrapil\WF@pspars%{\the\@tempdima \the\@tempdimb}% + \edef\@tempb{\@@parshape\c@WF@wrappedlines \WF@ps \the\@tempdima \the\@tempdimb}% + \expandafter\endgroup\@tempb} + +\let\@@setpar\@setpar +\def\WF@noil{\z@ \hsize} +\let\WF@pspars\@empty + +\def\WF@fudgeparshape{\relax \ifnum\c@WF@wrappedlines<\tw@ \WF@finale + \else \afterassignment\WF@fudgeparshapee \fam \fi} +\def\WF@fudgeparshapee{\ifnum\fam=\@ne \expandafter \WF@parshapeee \else + \WF@conflict \@@parshape\fam \fi} +\def\WF@parshapeee#1#2{\begingroup\delimitershortfall#1% + \nulldelimiterspace#2%\advance\nulldelimiterspace\WF@adjlw + \edef\@tempa{\def\noexpand\WF@pspars{% + \the\delimitershortfall \the\nulldelimiterspace}}% + \expandafter\endgroup\@tempa \WF@wraphand} + +\def\WF@finale{\ifx\parshape\WF@fudgeparshape + \WF@restoretol \let\@setpar\@@setpar \let\par\WF@@par + \advance\linewidth\WF@adjlw \advance\@totalleftmargin-\WF@adjtlm + \WF@info{Finish wrapping text}% + \ifx\par\@@par \def\@par{\let\par\@@par\par}\else \let\@par\WF@@par \fi + \let\parshape\@@parshape + \parshape\ifx\WF@pspars\@empty \z@ \else \@ne \WF@pspars\fi \fi + \ifvoid\WF@box \ifx\everypar\WF@everypar + \let\everypar\WF@@everypar \everypar\expandafter{\the\WF@everypar}% + \fi\fi} + +\newcommand{\WFclear}{\par + \ifvoid\WF@box\else \vskip\bigskipamount \box\WF@box + \let\everypar\WF@@everypar \everypar\expandafter{\the\WF@everypar}% + \fi \global\c@WF@wrappedlines\z@ \WF@finale} + +\begingroup + \toks0={\let\everypar\WF@@everypar \everypar\expandafter{\the\WF@everypar}% + \let\parshape\@@parshape \let\@setpar\@@setpar } + \toks1=\expandafter{\@arrayparboxrestore} + \toks2=\expandafter{\clearpage} + \edef\@tempa{\def\noexpand\@arrayparboxrestore{\the\toks0 \the\toks1}% + \def\noexpand\clearpage{\noexpand\protect\noexpand\WFclear \the\toks2}} + \expandafter +\endgroup\@tempa + +\@ifundefined{@capwidth}{\let\@capwidth\hsize}{}% Pamper RevTeX's Stupidity + +\def\WF@conflict{\WF@warning + {\WF@wfname used inside a conflicting environment}} +\def\WF@collision{\WF@warning{Collision between wrapping environments}} +\def\WF@fltmes{\ifWF@float \WF@info{\WF@wfname floats}% + \else \WF@warning{Stationary \WF@wfname forced to float}\fi} + +\let\WF@warning\@warning +\let\WF@info\@gobble + +% Support float.sty: float styles and \newfloat. Make \newfloat{foo} +% define the `wrapfoo' environment. Support \newfloat from memoir.cls +% and \newfloatlist from ccaption.sty. +% +\let\WF@floatstyhook\relax + +\@ifundefined{newfloat}{}{% There is a \newfloat command +% + \@ifundefined{restylefloat}{ + % \newfloat comes from somewhere besides float.sty + \@ifclassloaded{memoir}{ + \toks@=\expandafter\expandafter\expandafter + {\csname\string\newfloat\endcsname [{#1}]{#2}{#3}{#4}% + \newenvironment{wrap#2}{\wrapfloat{#2}}{\endwrapfloat}% + } + \edef\@tempa{\def\expandafter\noexpand\csname\string\newfloat\endcsname + [##1]##2##3##4{\the\toks@}} + \@tempa + }% end memoir support + {}% Other origins of \newfloat here?? + }{ + % float.sty handler. Ooops: Two versions for different versions + % Changing \float@restyle (or \restylefloat) changes \newfloat too. + \@ifundefined{float@restyle}{% older float.sty + \toks@=\expandafter{\restylefloat{#1}% (env may or may not be defined) + \@namedef{wrap#1}{\def\@captype{#1}\@nameuse{fst@#1}% + \def\WF@floatstyhook{\let\@currbox\WF@box \columnwidth\wd\WF@box + \global\setbox\WF@box\float@makebox}% + \@ifnextchar[\WF@wr{\WF@wr[]}}% + \expandafter\let\csname endwrap#1\endcsname \endwrapfigure + }\edef\@tempa{\def\noexpand\restylefloat##1{\the\toks@}} + }{% newer float.sty: use \float@restyle, and \float@makebox takes width arg + \toks@=\expandafter{\float@restyle{#1}% (env may or may not be defined) + \@namedef{wrap#1}{\def\@captype{#1}\@nameuse{fst@#1}% + \def\WF@floatstyhook{\let\@currbox\WF@box + \global\setbox\WF@box\float@makebox{\wd\WF@box}}% + \@ifnextchar[\WF@wr{\WF@wr[]}}% + \expandafter\let\csname endwrap#1\endcsname \endwrapfigure + }\edef\@tempa{\def\noexpand\float@restyle##1{\the\toks@}} + } + \@tempa % perform redefinitions + % + }% End float.sty handler +}% End redefinitions of \newfloat + +% Support ccaption.sty +\@ifundefined{\string\newfloatlist}{}{ + \toks@=\expandafter\expandafter\expandafter + {\csname\string\newfloatlist\endcsname [{#1}]{#2}{#3}{#4}{#5}% + \@namedef{wrap#2}{\wrapfloat{#2}}% + \expandafter\let\csname endwrap#2\endcsname \endwrapfloat + } + \edef\@tempa{\def\expandafter\noexpand\csname\string\newfloatlist\endcsname + [##1]##2##3##4##5{\the\toks@}} + \@tempa +} + +% Process package options. + +\@ifundefined{DeclareOption}{\endinput}{} + +\def\WF@warning{\PackageWarning{wrapfig}} +\ProvidesPackage{wrapfig}[2003/01/31 \space v 3.6] +\DeclareOption{verbose}{\def\WF@info{\PackageInfo{wrapfig}}} +\ProcessOptions +\AtEndDocument{\WFclear} + +\endinput + +%%%%% ----- End definitions ----- %%%%% + +%%%%% ----- Begin Instructions ----- %%%%% + + +W R A P F I G . S T Y \ \ ver 3.6 \ \ (Jan 31, 2003) + +Copyright (C) 1991-2003 by Donald Arseneau (asnd@triumf.ca) + +Wrapfig.sty provides the environments "wrapfigure" and "wraptable" for +typesetting a narrow float at the edge of the text, and making the text +wrap around it. The "wrapfigure" and "wraptable" environments interact +properly with the "\caption" command to produce proper numbering, but +they are not regular floats like "figure" and "table", so (beware!) they +may be printed out of sequence with the regular floats. There are four +parameters for "\begin{wrapfigure}", two optional and two required, plus +the text of the figure, with a caption perhaps: + + \begin{wrapfigure}[12]{r}[34pt]{5cm}
\end{wrapfigure} + == = ==== === + [number of narrow lines] {placement} [overhang] {width} + +Some idiosyncrasies: + + - You must not specify a wrapfigure in any type of list environment or + or immediately before or immediately after one. It is OK to follow + a list if there is a blank line ("\par") in between. + + - If you put a wrapfigure in a parbox or a minipage, or any other type + of grouping, the text wrapping should end before the group does. + + - It does work in two-column format, but are your figures that small? + + - It may be out of sequence with regular floats. + + - The hlines that may be printed above and below floats are ignored; + you must insert them manually if desired. + + - "\linewidth" is now adjusted within the wrapped text, but since it + can only be set for whole paragraphs at a time, it will persist with + the wrong value after the wrapping, until the paragraph is finished. + +New wrapping environments may be added when new float types are defined +(using memoir.cls, float.sty, or ccaption.sty). Any wrapping environment, +"wrapfigure", "wraptable", or something else may be invoked using the +"wrapfloat" environment, as in "\begin{wrapfloat}{figure}{O}{5cm}". + +To use float.sty properly, load package "float" before "wrapfig", +and declare any new float types after loading both. Likewise for +ccaption.sty and "\newfloatlist" and memoir.cls and its "\newfloat". + +\section{Placement and Floating} + +Parameter "#2" (required) is the figure placement code, but the valid +codes are different from regular figures. They come in pairs: an +uppercase version which allows the figure to float, and a lowercase +version that puts the figure ``exactly here''. + + r R - the right side of the text + l L - the left side of the text + i I - the inside edge--near the binding (if "[twoside]" document) + o O - the outside edge--far from the binding + +You should specify one code only, not a list. The figure or table must +be on one side or the other; it cannot be in the middle with text on +both sides. The "i" and "o" options refer to the inside and outside of +the whole page, not individual columns. + +The ability to float is somewhat restricted, and you will get best results +by giving exact manual placement, but floating is more convenient while +revising the document. Any changes to the formatting can ruin your manual +positioning so you should adjust the placement just before printing a +final copy. Here are some tips for good placement: + + - The environment should be placed so as to not run over a page break. + + - The environment must not be placed in special places like lists. + + - For esthetic reasons, only plain text should wrap around the figure. + Section titles and big equations look bad; lists are bad if the figure + is on the left. (All these function properly, they just don't look + very good.) Small equations look fine. + + - It is convenient to begin the environment between paragraphs, but if + you want placement in the middle of a paragraph, you must put the + environment between two words where there is a natural line break. + +When floating, \LaTeX\ tries to apply these rules. More specifically, +a floated wrapping environment will only begin... + + - at the beginning of a paragraph, + + - when there is enough room on the page, or it is possible to go on + the next page, + + - if the `paragraph' is not in a section title or a list, + + - if the paragraph is not wrapping around another figure, + + - in the main text (not in a minipage etc.) + +It is possible that a non-floating wrapfigure will be forced to float +when an earlier one is still being processed. A warning will be written +in that case. You can have more information about the floating process +written to the log file by specifying "\usepackage[verbose]{wrapfig}". + +If there is a lot of flexibility on a page, a floating wrapfigure may +be placed badly; you must turn to manual placement. A rare problem is +that floats and footnotes specified within the wrapping text can also +cause poor placement and bad formatting. + + +\section {Sizing and optional overhang} + +Parameter "#4" (the second required parameter) is the width of the figure +or table. Given the way that \LaTeX\ puts just about everything into boxes +with the current line-width, the width parameter will take precedence over +whatever natural width the figure has. In particular, the caption is always +typeset with the specified width. If the figure is wider than the space +allotted, you will get an ``overfull box'' warning. + +However, if you specify a width of *zero* ("0pt"), the actual width of +the figure will determine the wrapping width. A following "\caption" +should have the same width as the figure, but it might fail badly; it +is safer to specify a width when you use a caption. + +\LaTeX\ will wrap surrounding text around the figure, leaving a gap of +"\intextsep" at the top and bottom, and "\columsep" at the side, by +producing a series of shortened text lines beside the figure. The +indentation (shortening) of the text is the figure width plus "\columnsep" +minus overhang (if any; see below). + +\LaTeX\ calculates the number of short lines needed based on the height +of the figure and the length "\intextsep". You can override this guess +by giving the first optional argument (parameter "#1") specifying the +number of shortened lines (counting each displayed equation as 3 lines). +This is particularly useful when the surrounding text contains extra +vertical spacing that is not accounted for automatically. + +The second optional parameter ("#3") tells how much the figure should +hang out into the margin. The default overhang is given by the length +"\wrapoverhang", which is "0pt" normally but can be changed using +"\setlength". For example, to have all wrapfigures use the space +reserved for marginal notes, + + \setlength{\wrapoverhang}{\marginparwidth} + \addtolength{\wrapoverhang}{\marginparsep} + +When you do specify the overhang explicitly for a particular figure, you +can use a special unit called "\width" meaning the width of the figure. +For example, "[0.5\width]" makes the center of the figure sit on the +edge of the text, and "[\width]" puts the figure entirely in the margin +(and the adjacent text is indented by just "\columnsep"). This "\width" +is the actual width of the wrapfigure, which may be greater than the +declared width. + + +\section{Some Random Implementation Notes} + +Unfortunately, \LaTeX's system of setting "\everypar" and "\par" is +unable to coexist peacefully with a wrapping environment, so I was +forced to subvert the "\@setpar" mechanism and "\everypar". ("\everypar" +is already subverted once by NFSS.) + +When checking the room left on the page, remember that if there is less +than "\baselineskip" the new paragraph will begin on the next page, even +if there is no page stretch. If non-floating, I force a bad page break +rather than have the figure hang into the bottom margin. + +Here are notes on various variables and some macros; what info they +store and how they are used. + + \WF@wli - number-of-wrapped-lines parameter, saved for start of wrapping. + Set globally by "\WF@wr" (set empty if no optional parameter given). + The floating mechanism ignores this and uses the real size. + + \WF@ovh - margin overhang set globally by "\WF@rapt", saved until placing + figure (but not reset). Actually, the setting is very tricky so that + the expected values are used when a figure floats. First, the expression + is saved without evaluation by "\WF@rapt" ("\begin{wrapfigure}") because + "\width" is still unknown. Soon after that, "\endwrapfigure" executes + "\WF@ovh" to evaluate the overhang and save the result (so that changes + to "\wrapoverhang" while this figure is floating won't affect this + figure). Finally, it is used by "\WF@putfigmaybe" when printing the fig. + + \WF@place - a macro that is used as a number, giving the placement code. + It might start out as "`I" and later be converted to "114" (r). + + \WF@box - tested for void at "\begin{wrapfigure}", to avoid collisions, + by "\everypar" to do floating, and by "\WF@finale" before resetting + "\everypar". Voided globally when used by "\WF@putfigmaybe" (or by + "\WF@wr" if an old figure must be dumped prematurely). + + \par - test if it is "\@@par" by "\begin{wrapfigure}" and "\WF@floathand" + to float past special environments. It is set to "\@par" ("\WF@mypar") + by "\WF@startwrapping", and restored by an end-group (bad!) or by + "\WF@finale" (good). It is protected from change by redefining + "\@setpar". + + \parshape - let to "\WF@fudgeparshape" by "\WF@startwrapping", so lists + will continue wrapping; "\@@parshape" preserves the real "\parshape" + command, and it is restored by "\WF@finale" or "\@parboxrestore". + "\WF@floathand" and "\WF@wr" test if old wrapping is still in progress + with "\ifx\parshape\WF@fudgeparshape". The value of "\@@parshape" is + also tested to float past lists and other wrapping environments. + + \hangindent - tested to float past section titles etc. + + \c@WF@wrappedlines - the number of shortened lines + 1; set globally by + "\WF@startwrapping" and decremented by "\par" ("\WF@mypar"). It is > 1 + only when wrapping is incomplete. "\WF@wraphand", "\WF@fudgeparshape", + and "\WF@mypar" test the number for calling "\WF@finale". It may get + stuck at some high value if "\par" is restored by an end-group, (and + wrapping is terminated prematurely) so it is unwise to use this as a + test for wrapping-complete. + + \pagetotal - one of many parameters used to compute floating. When + putting a wrapfigure in a parbox, I assign "\let\pagetotal\maxdimen" + (locally!) to signal not-top-of-page and no floating. + + \WF@pspars - the "\parshape" parameters as LaTeX sets them for lists + ("\WF@fudgeparshape"); when wrapping I test it and use it to modify my + own real params for the paragraph. They are also used when "\parshape" + is restored after wrapping. + + \WF@finale - is performed by "\par" when wrapping should end. However, + that might happen inside a group (a list especially), so the subverted + versions of "\par", "\parshape" etc. will be reinstated when the group + ends. Thus, they must themselves test "\c@WF@wrappedlines" < 2 to see + when wrapping is over, and if so, they should just do "\WF@finale" again. + +These are the tests to see if a floating wrapfigure will fit at a particular +spot. These tests are performed at the beginning of every paragraph after +the figure, except in lists etc. ("\pagegoal" - "\pagetotal" is the room +left on the page.) + + > + room_left := \pagegoal - \pagetotal + if room_left < 0 then page overfull already: put figure (on next page) + else + if figure_size > room_left then does not fit + if max(min_stretch, \pagestretch) + extra > room_left + then page can stretch until full: put figure (at top of next page) + fi + else figure fits: put figure + fi fi + < + +Even if a wrapfigure is not floating, it will go through the same logic +to generate a "\pagebreak", and maybe an underfull page, when the current +page can stretch until full. The "min_stretch" depends on whether it is +floating or not: ".5\baselineskip" (floating) "2\baselineskip" (not). The +"extra" is ".5\baselineskip" in either case. 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Given the source representation of the target program and the +target program compiled in untyped lambda form, the algoritmhm is capable of modelling +the source program in terms of symbolic constraints on it's branches and apply symbolic +execution on the untyped lambda representation in order to validate wheter the compilation +produced a valid result. +In this context a valid result means that for every input in the domain of the source +program the untyped lambda translation produces the same output as the source program. +The input of the program is modelled in terms of symbolic constraints closely related to +the runtime representation of OCaml objects and the output consists of OCaml code +blackboxes that are not evaluated in the context of the verification. + +\end{abstract} + +* Introduction + +** TODO OCaml + Objective Caml (OCaml) is a dialect of the ML (Meta-Language) family of programming + languages. + OCaml shares many features with other dialects of ML, such as SML and Caml Light, + The main features of ML languages are the use of the Hindley-Milner type system that + provides with respect to static type systems of traditional imperative and/or object + oriented language such as C, C++ and Java many advantages such as: + - Parametric polymorphism: in certain scenarios a function can accept more than one + type for the input parameters. For example a function that computes the lenght of a + list doesn't need to inspect the type of the elements of the list and for this reason + a List.length function can accept list of integers, list of strings and in general + list of any type. Such languages offer polymorphic functions through subtyping at + runtime only, while other languages such as C++ offer polymorphism through compile + time templates and function overloading. + With the Hindley-Milner type system each well typed function can have more than one + type but always has a unique best type, called the /principal type/. + For example the principal type of the List.length function is "For any /a/, function from + list of /a/ to /int/" and /a/ is called the /type parameter/. + - Strong typing: Languages such as C and C++ allow the programmer to operate on data + without considering its type, mainly through pointers. Other languages such as C# + and Go allow type erasure so at runtime the type of the data can't be queried. + In the case of programming languages using an Hindley-Milner type system the + programmer is not allowed to operate on data by ignoring or promoting its type. + - Type Inference: the principal type of a well formed term can be inferred without any + annotation or declaration. diff --git a/tesi/prova.out b/tesi/prova.out new file mode 100644 index 0000000..946788b --- /dev/null +++ b/tesi/prova.out @@ -0,0 +1,3 @@ +\BOOKMARK [1][-]{section.1}{TODO Scaletta [1/2]}{}% 1 +\BOOKMARK [1][-]{section.2}{Introduction}{}% 2 +\BOOKMARK [2][-]{subsection.2.1}{TODO OCaml}{section.2}% 3 diff --git a/tesi/prova.pdf b/tesi/prova.pdf new file mode 100644 index 0000000000000000000000000000000000000000..85a9192e94b6d3fe8dd4d44b33b4ed0d02aad0ce GIT binary patch literal 133009 zcma&NQ;;r9(5>0rZQHhO+uCj8ZQHhO+qP}nwr%akd^2(WiHSIKaq24bx+2!9%x4vu zqNq3>6FnO=+5GazIy4(0BcYvjMi~= 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