Factoring Out Assumptions to Speed Up MUS Extraction

Abstract

Abstract. In earlier work on a limited form of extended resolution for CDCL based SAT solving, new literals were introduced to factor out parts of learned clauses. The main goal was to shorten clauses, reduce proof size and memory usage and thus speed up propagation and conflict analysis. Even though some reduction was achieved, the effectiveness of this technique was rather modest for generic SAT solving. In this paper we show that factoring out literals is particularly useful for incremental SAT solving, based on assumptions. This is the most common approach for incremental SAT solving and was pioneered by the authors of MINISAT. Our first contribution is to focus on factoring out only assumptions, and actually all eagerly. This enables the use of compact dedicated data structures, and naturally suggests a new form of clause minimization, our second contribution. As last main contribution, we propose to use these data structures to maintain a partial proof trace for learned clauses with assumptions, which gives us a cheap way to flush useless learned clauses. In order to evaluate the effectiveness of our techniques we implemented them within the version of MINISAT used in the publically available state-of-the-art MUS extractor MUSer. An extensive experimental evaluation shows that factoring out assumptions in combination with our novel clause minimization procedure and eager clause removal is particularly effective in reducing average clause size, improves running time and in general the state-of-the-art in MUS extraction.

Turbo-charging Lemmas on demand with don't care reasoning

“…However, this would require an interleaved execution between the primal and the dual solver, which is rather involved to implement and subject of future work. Further, our current version of dual propagation-based partial model extraction heavily relies on incremental SAT solving under assumptions, which can benefit from dedicated data structures [17]. The integration of such SAT solver level optimization techniques is also left to future work.…”

“…⊥), we follow both its condition and its then (resp. else) branch (lines [15][16][17][18][19][20]. In any other case where x is not an APPLY node, we follow all inputs of node x (line 22).…”

Efficient MUS extraction with resolution

“…We refer to a configuration of HaifaMUC that implements the deletion-based algorithm with incremental SAT and clause set refinement as Base. We compare our tool to the latest version of MUSer2 [7] and Minisatabb [18]. Extended experimental data is available from the second author's home page.…”

“…We show in Sect. III that, as a result, HaifaMUC now outperforms the leading MUS extractors MUSer2 and Minisatabb [18]. Minisatabb improves MUSer2 considerably based on the idea of replacing blocks of assumptions with new variables [18].…”

On Extracting Arguments in Favor of One Given Conclusion

“…Checking whether or not a CNF is a MUS is DP-complete [24] and checking whether or not a clause belongs to a MUS is in Σ P 2 [11]. Despite these bad worsttime complexity results, much progress has been obtained this last decade for the efficient extraction of MSSes, CoMSSes and MUSes from Δ in many cases (see for example [2,21,19,18,15]). …”