From b433663bdd3ad285097ab60bf2833be21c2c57b5 Mon Sep 17 00:00:00 2001 From: Francesco Mecca Date: Thu, 2 Apr 2020 14:14:39 +0200 Subject: [PATCH] latex symbols and python --- tesi/conv.py | 6 ++++-- tesi/tesi.pdf | Bin 363399 -> 363099 bytes tesi/tesi_unicode.org | 16 ++++++++-------- 3 files changed, 12 insertions(+), 10 deletions(-) diff --git a/tesi/conv.py b/tesi/conv.py index 120475a..ce5fd8b 100644 --- a/tesi/conv.py +++ b/tesi/conv.py @@ -3,10 +3,12 @@ import re from sys import argv allsymbols = json.load(open('./unicode-latex.json')) -mysymbols = ['≡', '≠', '≼', '→', '←', '⊀', '⋠', '≺', '∀', '∈', 'ε','₀', '₂', '₁', '₃', 'ₐ', 'ₖ', 'ₘ', 'ₙ', 'ᵢ', 'ⁱ', '⋮'] +mysymbols = ['≡', '≠', '≼', '→', '←', '⊀', '⋠', '≺', '∀', '∈', 'ε','₀', '₂', '₁', '₃', 'ₐ', 'ₖ', 'ₘ', 'ₙ', 'ᵢ', 'ⁱ', '⋮', 'ₛ', 'ₜ', '≃', '⇔', '∧', '∅', 'ℕ', 'ⱼ', 'ʲ', '⊥', 'π'] +extrasymbols = {'〚': '\llbracket', '〛': '\rrbracket'} symbols = {s: allsymbols[s] for s in mysymbols} -mathsymbols = {s: '$'+allsymbols[s]+'$' for s in symbols} +symbols.update(extrasymbols) +mathsymbols = {s: '$'+v+'$' for s, v in symbols.items()} def read_by_char(fname): # Yield character and True/False if inside mathmode block diff --git a/tesi/tesi.pdf b/tesi/tesi.pdf index 8c6afeacd8a84c5473659eaf5bf62c584b2e3778..ac6cb94ed00ac01035752872bbad5ee1e5723668 100644 GIT binary patch delta 76799 zcmV)DK*7IlVPYSf9+aZZ|lYpem}oLc?wk=G2HvoK_A+*X%Hki zL13ULl0487ZLx3RRcoT-n9tX7OXh;^ohmUk|S>eq5;}iQY83f2>=s zWTK;H$)bIkUo2NDWl^`yn;ajgD5D!4-7OW4ihAGDleTNJF25=AmI$uvh8}G4tSqV< zn!PW&E#1|?qFDjQE^n&V2?WB%HWiB%T$M~o*2^t$6xKwyb=%>cjjF7;TXGxaG^{I6 zQM5GC)iiE*Wzo@Xx9y1^d4d4(e{!W+5`DR}JVJSqG=Io$ccou4qqmwG`Q6iC=VVPt zOhrk28ltf<_#3c;hS!YdoGyudfXLTYTGRK<)lSS^hc<3IYRL?uKk<(O8+TykLT zh;~H5<-)|NNgRQSrA=Y2SPM;5#pj-kO~|-V{W{EZQd3Swh{b4~|Ayode{mxEWqt{W zBV%j+9BG=MG%4rrCJuXA9IzLA)?S}4S4^9r+29o+PSlj{*W+Q1M)0v{p6kWMg}c*1 z{u~4~ddB}YWC^Arji@n$PeNiqXrv3ZStI^e7Lqge-1aBd_xahW^lBga$RQoHmAwktZNEL3J<{#0{&bXAEx%C 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zC+}>lSgXi=U6$)L|K7o0&ga?KD_42CE-7VPD)q|gP;0&5dn&uW@;q1Le+0!oS;pOt zsPsZt;^#oKYwkR=m-UO*1|wPC`m8O~g^YLKa~9+W`zRFRdA@y(8{;viKeE^CIp+{6 zVBqyMpIa&qey}L0;Dr;qXDp8fitY5PN(DNP`pMqDsBs<&F&+vFU<#373bVX+mSYwu zLLVuDCo2}mM>oHo9M}ATB!Vk&{r?ru$=T4++1=6944#dXm7R?Ro`OPLK?44N0pvsr A)c^nh diff --git a/tesi/tesi_unicode.org b/tesi/tesi_unicode.org index 54291e5..d967388 100644 --- a/tesi/tesi_unicode.org +++ b/tesi/tesi_unicode.org @@ -921,17 +921,17 @@ Theorem: Given an input space /S/ and a couple of decision trees, where the target decision tree Cₜ covers the input space /S/, we say that the two decision trees are equivalent when: -| (equiv S Cₛ Cₜ gs = Yes) ∧ covers(Cₜ, S) ⇒ ∀vₛ≃vₜ ∈ S, Cₛ(vₛ) ≃gs Cₜ(vₜ) +| equiv(S, Cₛ, Cₜ, gs) = Yes ∧ covers(Cₜ, S) → ∀vₛ≃vₜ ∈ S, Cₛ(vₛ) ≃gs Cₜ(vₜ) Similarly we say that a couple of decision trees in the presence of an input space /S/ are /not/ equivalent when: -| (equiv S Cₛ Cₜ gs = No(vₛ,vₜ) ∧ covers(Cₜ, S) ⇒ vₛ≃vₜ ∈ S ∧ Cₛ(vₛ) ≠gs Cₜ(vₜ) +| equiv(S, Cₛ, Cₜ, gs) = No(vₛ,vₜ) ∧ covers(Cₜ, S) → vₛ≃vₜ ∈ S ∧ Cₛ(vₛ) ≠gs Cₜ(vₜ) Corollary: For a full input space /S/, that is the universe of the target program we say: -| (equiv S [|tₛ|]ₛ [|tₜ|]ₜ ∅ = Yes) ⇔ tₛ ≃ tₜ +| equiv(S, 〚tₛ〛ₛ, 〚tₜ〛ₜ, ∅) = Yes ⇔ tₛ ≃ tₜ *** Proof of the correctness of the translation from source programs to source decision trees @@ -1011,13 +1011,13 @@ we can say that the couple of decision trees are the same for every couple of source value /vₛ/ and target value /vₜ/ that are equivalent. \begin{comment} Define "covered" -Is it correct to say the same? How to correctly distinguish in words ≊ and = ? +Is it correct to say the same? How to correctly distinguish in words ≃ and = ? \end{comment} -| equiv(S, Cₛ, Cₜ) = Yes and cover(Cₜ, S) → ∀ vₛ ≊ vₜ∈S ∧ Cₛ(vₛ) = Cₜ(vₜ) +| equiv(S, Cₛ, Cₜ) = Yes and cover(Cₜ, S) → ∀ vₛ ≃ vₜ∈S ∧ Cₛ(vₛ) = Cₜ(vₜ) In the case where the algorithm returns No we have at least a couple of counter example values vₛ and vₜ for which the two decision trees outputs a different result. -| equiv(S, Cₛ, Cₜ) = No(vₛ,vₜ) and cover(Cₜ, S) → ∀ vₛ ≊ vₜ∈S ∧ Cₛ(vₛ) ≠ Cₜ(vₜ) +| equiv(S, Cₛ, Cₜ) = No(vₛ,vₜ) and cover(Cₜ, S) → ∀ vₛ ≃ vₜ∈S ∧ Cₛ(vₛ) ≠ Cₜ(vₜ) We define the following | Forall(Yes) = Yes @@ -1054,10 +1054,10 @@ In the other subcases S is always non-empty. subtree Cₜᵢ | equiv(Sᵢ, Cₛ, Cₜᵢ) = Yes ∀i or we have a counter example vₛ, vₜ for which - | vₛ≊vₜ∈Sₖ ∧ cₛ(vₛ) ≠ Cₜₖ(vₜ) + | vₛ≃vₜ∈Sₖ ∧ cₛ(vₛ) ≠ Cₜₖ(vₜ) then because | vₜ∈(a→πₖ) ⇒ Cₜ(vₜ) = Cₜₖ(vₜ) then - | vₛ≊vₜ∈S ∧ Cₛ(vₛ)≠Cₜ(vₜ) + | vₛ≃vₜ∈S ∧ Cₛ(vₛ)≠Cₜ(vₜ) and the result of the algorithm is | equiv(Sᵢ, Cₛ, Cₜᵢ) = No(vₛ, vₜ) for some minimal k∈I