Anton Belov

Anton Belov, Antonio Morgado, Joao Marques-Silva

State-of-the-art algorithms for industrial instances of MaxSAT problem rely on iterative calls to a SAT solver. Preprocessing is crucial for the acceleration of SAT solving, and the key preprocessing techniques rely on the application of resolution and subsumption elimination. Additionally, satisfiability-preserving clause elimination procedures are often used. Since MaxSAT computation typically involves a large number of SAT calls, we are interested in whether an input instance to a MaxSAT problem can be preprocessed up-front, i.e. prior to running the MaxSAT solver, rather than (or, in addition to) during each iterative SAT solver call. The key requirement in this setting is that the preprocessing has to be sound, i.e. so that the solution can be reconstructed correctly and efficiently after the execution of a MaxSAT algorithm on the preprocessed instance. While, as we demonstrate in this paper, certain clause elimination procedures are sound for MaxSAT, it is well-known that this is not the case for resolution and subsumption elimination. In this paper we show how to adapt these preprocessing techniques to MaxSAT. To achieve this we recast the MaxSAT problem in a recently introduced labelled-CNF framework, and show that within the framework the preprocessing techniques can be applied soundly. Furthermore, we show that MaxSAT algorithms restated in the framework have a natural implementation on top of an incremental SAT solver. We evaluate the prototype implementation of a MaxSAT algorithm WMSU1 in this setting, demonstrate the effectiveness of preprocessing, and show overall improvement with respect to non-incremental versions of the algorithm on some classes of problems.

Anton Belov, Joao Marques-Silva

Detection and elimination of redundant clauses from propositional formulas in Conjunctive Normal Form (CNF) is a fundamental problem with numerous application domains, including AI, and has been the subject of extensive research. Moreover, a number of recent applications motivated various extensions of this problem. For example, unsatisfiable formulas partitioned into disjoint subsets of clauses (so-called groups) often need to be simplified by removing redundant groups, or may contain redundant variables, rather than clauses. In this report we present a generalized theoretical framework of labelled CNF formulas that unifies various extensions of the redundancy detection and removal problem and allows to derive a number of results that subsume and extend previous work. The follow-up reports contain a number of additional theoretical results and algorithms for various computational problems in the context of the proposed framework.