Automatic Detection of At-Most-One and Exactly-One Relations for Improved SAT Encodings of Pseudo-Boolean Constraints

Pseudo-Boolean (PB) constraints often have a critical role in constraint satisfaction and optimisation problems. Encoding PB constraints to SAT has proven to be an efficient approach in many applications, however care must be taken to encode them compactly and with good propagation properties. It has been shown that at-most-one (AMO) and exactly-one (EO) relations over subsets of the variables can be exploited in various encodings of PB constraints, improving their compactness and solving performance. In this paper we detect AMO and EO relations completely automatically and exploit them to improve SAT encodings that are based on Multi-Valued Decision Diagrams (MDDs). Our experiments show substantial reductions in encoding size and dramatic improvements in solving time thanks to automatic AMO and EO detection

Eliminating redundant clauses in SAT instances

In this paper, we investigate to which extent the elimination of a class of redundant clauses in SAT instances could improve the efficiency of modern satisfiability provers. Since testing whether a SAT instance does not contain any redundant clause is NP-complete, a logically incomplete but polynomial-time procedure to remove redundant clauses is proposed as a pre-treatment of SAT solvers. It relies on the use of the linear-time unit propagation technique and often allows for significant performance improvements of the subsequent satisfiability checking procedure for really difficult real-world instances.Anglai

Formula Preprocessing in MUS Extraction

Efficient algorithms for extracting minimally unsatisfiable subformulas (MUSes) of Boolean formulas find a wide range of applications in the analysis of systems, e.g., hardware and software bounded model checking. In this paper we study the applicability of preprocessing techniques for Boolean satisfiability (SAT) in the context of MUS extraction. Preprocessing has proven to be extremely important in enabling more efficient SAT solving. Hence the study of the applicability and the effectiveness of preprocessing in MUS extraction is highly relevant. Considering the extraction of both standard and group MUSes, we focus on a number of SAT preprocessing techniques, and formally prove to what extent the techniques can be directly applied in the context of MUS extraction. Furthermore, we develop a generic theoretical framework that captures MUS extraction problems, and enables formalizing conditions for correctness-preserving applications of preprocessing techniques that are not applicable directly. We experimentally evaluate the effect of preprocessing in the context of group MUS extraction

On computing minimal equivalent subformulas

A propositional formula in Conjunctive Normal Form (CNF) may contain redundant clauses | clauses whose removal from the for- mula does not a ect the set of its models. Identi cation of redundant clauses is important because redundancy often leads to unnecessary com- putation, wasted storage, and may obscure the structure of the problem. A formula obtained by the removal of all redundant clauses from a given CNF formula F is called a Minimal Equivalent Subformula (MES) of F. This paper proposes a number of e cient algorithms and optimization techniques for the computation of MESes. Previous work on MES com- putation proposes a simple algorithm based on iterative application of the de nition of a redundant clause, similar to the well-known deletion- based approach for the computation of Minimal Unsatis able Subfor- mulas (MUSes). This paper observes that, in fact, most of the existing algorithms for the computation of MUSes can be adapted to the compu- tation of MESes. However, some of the optimization techniques that are crucial for the performance of the state-of-the-art MUS extractors cannot be applied in the context of MES computation, and thus the resulting algorithms are often not e cient in practice. To address the problem of e cient computation of MESes, the paper develops a new class of al- gorithms that are based on the iterative analysis of subsets of clauses. The experimental results, obtained on representative problem instances, con rm the e ectiveness of the proposed algorithms. The experimental results also reveal that many CNF instances obtained from the practical applications of SAT exhibit a large degree of redundancy