From 02031babecec6ac3d73914273bfda5c84df68095 Mon Sep 17 00:00:00 2001 From: Spencer Killen Date: Sun, 14 May 2023 11:13:05 -0600 Subject: [PATCH] add a approximator for partial stable semantics --- document.pdf | Bin 185406 -> 186260 bytes document.tex | 10 ++++++++++ 2 files changed, 10 insertions(+) diff --git a/document.pdf b/document.pdf index 52564cb85bed4067d485d44d7b173ee7b16c694e..5667997218e5647ce17d63878327cf6f99cada28 100644 GIT binary patch delta 48000 zcmV(^K-Is#s0);@3$Uvn1Ti!+HIs3xD1Yr(OK;;g5WerP5PGsvn9KKLgC1OX;quU@}ZHe-x9rFgcu z%$N|wXq#ze2p1|_tg{~{g0Sg~F|H=_YC01JzSq}HJr!*7vE1cd-QehD-#GVEd4JQD z`4$J>clmN##CEaEtEu3Vu3WX#pBCT0e#>d*h|^qq6NDiOESPaigg44ta6u`(po&Iu zF%oB#Fv>EDf{W?Qipd$6s|}cOUpuqJ>RuXDGB1;9q9xBL5mMvKn=s5lwa8|p@vovv zeQ1GVgU-u@jgmOadx1@nuM>uGN`I^v8J0S$Al9f}rb#G~#29vbx+8N9VQx_JYho8o zsCCD?9BNR)_5yr5N+RjVZqCyeJ#zE1Uf-b*b6~MEV38Mc 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\wp(\mathcal{L}), \subseteq \rangle$ whose least element is $\emptyset$. \end{definition} + \subsection{An Approximator for Partial Stable Semantics} + + \begin{align*} + \Gamma(T, P) &\define \{ \head(r) ~|~ r \in \P, T \subseteq \bodyp(r), \bodyn(r) \intersect P = \emptyset \}\\ + \Gamma(P, T) &\define \{ \head(r) ~|~ r \in \P, P \subseteq \bodyp(r), \bodyn(r) \intersect T = \emptyset \}\\ + \Phi(T, P) &\define \Bigl( \Gamma(T, P), \Gamma(P, T) \Bigr) + \end{align*} + + \section{The Polynomial Heirarchy} Intuitive definitions of ${\sf NP}$ \begin{itemize} @@ -176,4 +185,5 @@ \item (Alternating Turing machine) A problem that is solved by some path of an algorithm that is allowed to branch in parallel. A branch is allowed to switch to ``ALL'' mode only once and require that all subsequent forks return success \end{itemize} + \end{document} \ No newline at end of file