From 29e7ae26b9261ff76f5fd326d4125362800cca08 Mon Sep 17 00:00:00 2001 From: Francesco Mecca Date: Tue, 8 Jan 2019 16:42:33 +0100 Subject: [PATCH] mcad seminario --- anno2/mie/Mcad/ScalettaMCAD.txt | 21 ++++++++++----------- anno2/mie/Mcad/ben1983another.pdf | Bin 0 -> 248113 bytes anno2/mie/Mcad/benor.odp | Bin 20230 -> 23810 bytes anno2/mie/Mcad/relazione_mcad.md | 20 +++++++++++++++++++- 4 files changed, 29 insertions(+), 12 deletions(-) create mode 100644 anno2/mie/Mcad/ben1983another.pdf diff --git a/anno2/mie/Mcad/ScalettaMCAD.txt b/anno2/mie/Mcad/ScalettaMCAD.txt index a3e442f..ee74216 100644 --- a/anno2/mie/Mcad/ScalettaMCAD.txt +++ b/anno2/mie/Mcad/ScalettaMCAD.txt @@ -1,11 +1,10 @@ -Introduzione al problema con esempi -Equivalenza fra modelli con cenni di dimostrazione -Definizione agreement -Well-formedness, validity, failure free-termination -Definizione formale problema -Teorema 21.2 con dimostrazione -Algoritmo randomizzato definizione -Algoritmo di BenOr -Ottimizzazioni per BenOr -Failure detector -Modellazione failure detector \ No newline at end of file +Introduzione al problema con esempi +Equivalenza fra modelli con cenni di dimostrazione +Definizione agreement e Definizione formale problema +Well-formedness, validity, failure free-termination +Teorema 21.2 con dimostrazione -> vedi p 586, dimostrazione in termini degli altri due teoremi +Algoritmo randomizzato definizione +Algoritmo di BenOr +Ottimizzazioni per BenOr +Failure detector +Modellazione failure detector diff --git a/anno2/mie/Mcad/ben1983another.pdf b/anno2/mie/Mcad/ben1983another.pdf new file mode 100644 index 0000000000000000000000000000000000000000..4a1eef4df772ff31c01f888bd78b76624dfb8873 GIT binary patch literal 248113 zcmbsP2RxhY+dqzXs8O2^tAtvu+Od_!UO~;45;0n_tG1FNMp3iFUL|Tq+n^|^XiK+B ziAG6vBGu3enna`(TJp=K#(T;s}o31m;GS_@&*~`YlF1de?Hr-Kw4mZ zO-*g~qa{dBLtk5q{p1J&v;VuXf6~>_)B*9En1J|$A_BLE2L1n95~737^0QZ{WdP#W z__Jv0f_^`NBKY_IS!JN5|DSc5TDpI0r>U!{@waw*?6Lo2JWYM@-^Vl1`&(Zv4FkRZ 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un valore v "buono" se almeno f+1 messaggi del tipo ("first", s, *) contengono lo stesso valore v. +Ci possono essere al piu` due valori buoni. +(Se c'e` un solo valore buono v allora in ogni messaggio del tipo ("second", s, *) contiene il valore null o il valore v.) +(Se se ci sono due valore buoni allora in ogni messaggio del tipo ("second", s, *) contiene il valore null e x viene scelto a caso.) + +Nel caso in cui vi sia un solo valore buono, allora con probabilita` 1/2^n tutti i processi sceglieranno un valore x identico al valore buono. +Allo stesso modo, nel caso ci fossero due valori buoni, con probabilita` 1/2^n tutti i processi sceglieranno lo stesso valore x. +(In entrambi i casi i processi avranno lo stesso valore x con probabilita` 1/2^n.) +Dato che le probabilita` ad ogni iterazione sono indipendenti, possiamo combinarle per ottenere che: +1 - (probabilita` che almeno un processo non sia d'accordo su ogni iterazione) = 1 - (1 - 1/2^n)^s, ovvero la probabilita` che i processi decidano allo stage s+1. + + + + + + Aggiunte: Aguilera: -- Nel paper si mostra (in maniera intuitiva) perche` la probabilita` di terminazione e` 1. - C'e` una variante dove alla fine della fase 2 viene lanciato un "global coin", ovvero il numero casuale e` lo stesso per tutti i processi che lo richiedono. Questo accorcia di molto il tempo di esecuzione del programma a costo di avere n/3 < f < n/2 . - Lo scopo del paper e` di dimostrare che BenOr funzion con n >= 2f (piuttosto che 3f per la Lynch)