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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 the theory. And it \textbf{produces formal proofs}. } -\tblock{Conflict Driven Clause learning} +\tblock{Conflict Driven Clause Learning} { \begin{description} \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 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. \item[Conflict] A conflict is a clause $C$ that is false in the current partial model. \item[Analyze] Perform resolution between the analyzed clause and the reason 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 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 @@ -85,17 +85,17 @@ \begin{itemize}[label=\checkmark] \item Functorized design, using generative functors \item Local assumptions - \item Model output and Proof output (Coq, dot) + \item Model output and proof output (Coq, dot) \end{itemize} \end{itemize} } -\cblock{Solver interface} +\cblock{Solver Interface} { \inputminted{ocaml}{solver_intf.ml} } -\tblock{Other solvers} +\tblock{Other Solvers} { \begin{center} \begin{tabular}{c@{\quad}|@{\quad}c@{\quad}|@{\quad}c@{\quad}|@{\quad}c} @@ -111,19 +111,19 @@ \columnbreak -\tblock{Problem example} +\tblock{Problem Example} { - \vspace{.5cm} + \vspace{.2cm} \[ \begin{matrix} - H1: & a = b & \quad & H2: & b = c \lor b = d \\ - H3: & a <> d & \quad & H4: & a <> c \\ + \text{Are the following} & \quad & H1: & a = b & \quad & H2: & b = c \lor b = d \\ + \text{hypotheses satisfible ?} & \quad & H3: & a <> d & \quad & H4: & a <> c \\ \end{matrix} \] \includegraphics[height=33cm]{proof} } -\cblock{Theory interface} +\cblock{Theory Interface} { \inputminted{ocaml}{theory_intf.ml} } @@ -131,33 +131,34 @@ \tblock{Proof generation} { \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 \item Minimal impact on proof search (already done to compute unsat-core) \item Sufficient to rebuild the whole resolution tree \item A proof is a clause and proof nodes are expanded on demand\\ $\rightarrow$ no memory issue - \item Enables various proof output: + \item Enables various proof outputs: \begin{itemize}[label=$\bullet$] \item Dot/Graphviz (see example above) - \item Coq formal proof + \item Coq (and soon dedukti) formal proofs \end{itemize} \end{itemize} } \tblock{Performances} { + \\ \\ \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 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/hole7 & 4.257 & 0.213 & 0.015 & 0.073 \\ \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/hole10 & \begin{tabular}{c}timeout\\(600)\end{tabular} & 161.478 & \begin{tabular}{c}9.579 (minisat)\\160.376 (sattools)\end{tabular} & 72.050 \\ + pigeon/hole9 & timeout (600) & 8.886 & 0.634 & 4.075 \\ \hline + pigeon/hole10 & timeout (600) & 161.478 & \begin{tabular}{c}9.579 {\small (minisat)}\\160.376 {\small (sattools)}\end{tabular} & 72.050 \\ \end{tabular} }