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Final update (hopefully)

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Guillaume Bury 2017-09-04 12:18:31 +02:00
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{ {
\vspace{0.5cm} % Pour pas se faire manger par le titre \vspace{0.5cm} % Pour pas se faire manger par le titre
\msat{}: a SAT solving library in OCaml. Solves the \textbf{satisfibility} \msat{}: a SAT solving library in OCaml. It solves the \textbf{satisfibility}
of propositional clauses. It is \textbf{Modular}: the user provides of propositional clauses. It is \textbf{Modular}: the user provides
the theory. And it \textbf{produces formal proofs}. the theory. And it \textbf{produces formal proofs}.
} }
\tblock{Conflict Driven Clause learning} \tblock{Conflict Driven Clause Learning}
{ {
\begin{description} \begin{description}
\item[Propagation] If there exists a clause $C = C' \lor a$, where \item[Propagation] If there exists a clause $C = C' \lor a$, where
$C'$ is false in the partial model, then add $a \mapsto \top$ to $C'$ is false in the partial model, then add $a \mapsto \top$ to
the partial model, and record $C$ as the reason for $a$. the partial model, and record $C$ as the reason for $a$.
\item[Decision] Take an atom $a$ which is not yet in the partial model, \item[Decision] Take an atom $a$ that is not yet in the partial model,
and add $a \mapsto \top$ to the model. and add $a \mapsto \top$ to the model.
\item[Conflict] A conflict is a clause $C$ that is false in the current partial \item[Conflict] A conflict is a clause $C$ that is false in the current partial
model. model.
\item[Analyze] Perform resolution between the analyzed clause and the reason \item[Analyze] Perform resolution between the analyzed clause and the reason
behind the propagation of its most recently assigned litteral, until behind the propagation of its most recently assigned litteral, until
the analyzed clause is suitable for backumping the analyzed clause is suitable for backumping.
\item[Backjump] A clause is suitable for backjumping if its most recently \item[Backjump] A clause is suitable for backjumping if its most recently
assigned litteral $a$ is a decision. We can then backtrack to before the assigned litteral $a$ is a decision. We can then backtrack to before the
decision, and add the analyzed clause to the solver, which will then enable decision, and add the analyzed clause to the solver, which will then enable
@ -85,17 +85,17 @@
\begin{itemize}[label=\checkmark] \begin{itemize}[label=\checkmark]
\item Functorized design, using generative functors \item Functorized design, using generative functors
\item Local assumptions \item Local assumptions
\item Model output and Proof output (Coq, dot) \item Model output and proof output (Coq, dot)
\end{itemize} \end{itemize}
\end{itemize} \end{itemize}
} }
\cblock{Solver interface} \cblock{Solver Interface}
{ {
\inputminted{ocaml}{solver_intf.ml} \inputminted{ocaml}{solver_intf.ml}
} }
\tblock{Other solvers} \tblock{Other Solvers}
{ {
\begin{center} \begin{center}
\begin{tabular}{c@{\quad}|@{\quad}c@{\quad}|@{\quad}c@{\quad}|@{\quad}c} \begin{tabular}{c@{\quad}|@{\quad}c@{\quad}|@{\quad}c@{\quad}|@{\quad}c}
@ -111,19 +111,19 @@
\columnbreak \columnbreak
\tblock{Problem example} \tblock{Problem Example}
{ {
\vspace{.5cm} \vspace{.2cm}
\[ \[
\begin{matrix} \begin{matrix}
H1: & a = b & \quad & H2: & b = c \lor b = d \\ \text{Are the following} & \quad & H1: & a = b & \quad & H2: & b = c \lor b = d \\
H3: & a <> d & \quad & H4: & a <> c \\ \text{hypotheses satisfible ?} & \quad & H3: & a <> d & \quad & H4: & a <> c \\
\end{matrix} \end{matrix}
\] \]
\includegraphics[height=33cm]{proof} \includegraphics[height=33cm]{proof}
} }
\cblock{Theory interface} \cblock{Theory Interface}
{ {
\inputminted{ocaml}{theory_intf.ml} \inputminted{ocaml}{theory_intf.ml}
} }
@ -131,33 +131,34 @@
\tblock{Proof generation} \tblock{Proof generation}
{ {
\begin{itemize}[label=\checkmark] \begin{itemize}[label=\checkmark]
\item Each clause records its "history", that is the clauses \item Each clause records its "history" which is the clauses
used during analyzing used during analyzing
\item Minimal impact on proof search (already done to compute \item Minimal impact on proof search (already done to compute
unsat-core) unsat-core)
\item Sufficient to rebuild the whole resolution tree \item Sufficient to rebuild the whole resolution tree
\item A proof is a clause and proof nodes are expanded on demand\\ \item A proof is a clause and proof nodes are expanded on demand\\
$\rightarrow$ no memory issue $\rightarrow$ no memory issue
\item Enables various proof output: \item Enables various proof outputs:
\begin{itemize}[label=$\bullet$] \begin{itemize}[label=$\bullet$]
\item Dot/Graphviz (see example above) \item Dot/Graphviz (see example above)
\item Coq formal proof \item Coq (and soon dedukti) formal proofs
\end{itemize} \end{itemize}
\end{itemize} \end{itemize}
} }
\tblock{Performances} \tblock{Performances}
{ {
\\ \\
\begin{tabular}{c|@{\,}c@{\,}|@{\,}c@{\,}|c|c} \begin{tabular}{c|@{\,}c@{\,}|@{\,}c@{\,}|c|c}
solvers & aez & mSAT & \begin{tabular}{c}minisat\\(minisat/sattools)\end{tabular} & \begin{tabular}{c}cryptominisat\\(sattools)\end{tabular} \\ \hline solvers & \begin{tabular}{c}Alt-ergo-zero\\{\small aez}\end{tabular} & \begin{tabular}{c}mSAT\\{\small msat}\end{tabular} & \begin{tabular}{c}minisat\\{\small (minisat/sattools)}\end{tabular} & \begin{tabular}{c}cryptominisat\\{\small (sattools)}\end{tabular} \\ \hline
uuf100 (1000 pbs) & 0.125 & 0.012 & 0.004 & 0.006 \\ \hline uuf100 (1000 pbs) & 0.125 & 0.012 & 0.004 & 0.006 \\ \hline
uuf125 (100 pbs) & 2.217 & 0.030 & 0.006 & 0.013 \\ \hline uuf125 (100 pbs) & 2.217 & 0.030 & 0.006 & 0.013 \\ \hline
uuf150 (100 pbs) & TODO & TODO & TODO & TODO \\ \hline uuf150 (100 pbs) & 67.563 & 0.087 & 0.017 & 0.045 \\ \hline
pigeon/hole6 & 0.120 & 0.018 & 0.006 & 0.006 \\ \hline pigeon/hole6 & 0.120 & 0.018 & 0.006 & 0.006 \\ \hline
pigeon/hole7 & 4.257 & 0.213 & 0.015 & 0.073 \\ \hline pigeon/hole7 & 4.257 & 0.213 & 0.015 & 0.073 \\ \hline
pigeon/hole8 & 31.450 & 0.941 & 0.096 & 2.488 \\ \hline pigeon/hole8 & 31.450 & 0.941 & 0.096 & 2.488 \\ \hline
pigeon/hole9 & \begin{tabular}{c}timeout\\(600)\end{tabular} & 8.886 & 0.634 & 4.075 \\ \hline pigeon/hole9 & timeout (600) & 8.886 & 0.634 & 4.075 \\ \hline
pigeon/hole10 & \begin{tabular}{c}timeout\\(600)\end{tabular} & 161.478 & \begin{tabular}{c}9.579 (minisat)\\160.376 (sattools)\end{tabular} & 72.050 \\ pigeon/hole10 & timeout (600) & 161.478 & \begin{tabular}{c}9.579 {\small (minisat)}\\160.376 {\small (sattools)}\end{tabular} & 72.050 \\
\end{tabular} \end{tabular}
} }