On Using Unsatisfiability for Solving Maximum Satisfiability

Maximum Satisfiability (MaxSAT) is a well-known optimization pro- blem, with several practical applications. The most widely known MAXS AT algorithms are ineffective at solving hard problems instances from practical application domains. Recent work proposed using efficient Boolean Satisfiability (SAT) solvers for solving the MaxSAT problem, based on identifying and eliminating unsatisfiable subformulas. However, these algorithms do not scale in practice. This paper analyzes existing MaxSAT algorithms based on unsatisfiable subformula identification. Moreover, the paper proposes a number of key optimizations to these MaxSAT algorithms and a new alternative algorithm. The proposed optimizations and the new algorithm provide significant performance improvements on MaxSAT instances from practical applications. Moreover, the efficiency of the new generation of unsatisfiability-based MaxSAT solvers becomes effectively indexed to the ability of modern SAT solvers to proving unsatisfiability and identifying unsatisfiable subformulas

Boolean Satisfiability in Electronic Design Automation

Boolean Satisfiability (SAT) is often used as the underlying model for a significant and increasing number of applications in Electronic Design Automation (EDA) as well as in many other fields of Computer Science and Engineering. In recent years, new and efficient algorithms for SAT have been developed, allowing much larger problem instances to be solved. SAT “packages” are currently expected to have an impact on EDA applications similar to that of BDD packages since their introduction more than a decade ago. This tutorial paper is aimed at introducing the EDA professional to the Boolean satisfiability problem. Specifically, we highlight the use of SAT models to formulate a number of EDA problems in such diverse areas as test pattern generation, circuit delay computation, logic optimization, combinational equivalence checking, bounded model checking and functional test vector generation, among others. In addition, we provide an overview of the algorithmic techniques commonly used for solving SAT, including those that have seen widespread use in specific EDA applications. We categorize these algorithmic techniques, indicating which have been shown to be best suited for which tasks

Incremental Cardinality Constraints for MaxSAT

Maximum Satisfiability (MaxSAT) is an optimization variant of the Boolean Satisfiability (SAT) problem. In general, MaxSAT algorithms perform a succession of SAT solver calls to reach an optimum solution making extensive use of cardinality constraints. Many of these algorithms are non-incremental in nature, i.e. at each iteration the formula is rebuilt and no knowledge is reused from one iteration to another. In this paper, we exploit the knowledge acquired across iterations using novel schemes to use cardinality constraints in an incremental fashion. We integrate these schemes with several MaxSAT algorithms. Our experimental results show a significant performance boost for these algo- rithms as compared to their non-incremental counterparts. These results suggest that incremental cardinality constraints could be beneficial for other constraint solving domains.Comment: 18 pages, 4 figures, 1 table. Final version published in Principles and Practice of Constraint Programming (CP) 201

Efficient Haplotype Inference with Pseudo-Boolean Optimization

Abstract. Haplotype inference from genotype data is a key computational problem in bioinformatics, since retrieving directly haplotype information from DNA samples is not feasible using existing technology. One of the methods for solving this problem uses the pure parsimony criterion, an approach known as Haplotype Inference by Pure Parsimony (HIPP). Initial work in this area was based on a number of different Integer Linear Programming (ILP) models and branch and bound algorithms. Recent work has shown that the utilization of a Boolean Satisfiability (SAT) formulation and state of the art SAT solvers represents the most efficient approach for solving the HIPP problem. Motivated by the promising results obtained using SAT techniques, this paper investigates the utilization of modern Pseudo-Boolean Optimization (PBO) algorithms for solving the HIPP problem. The paper starts by applying PBO to existing ILP models. The results are promising, and motivate the development of a new PBO model (RPoly) for the HIPP problem, which has a compact representation and eliminates key symmetries. Experimental results indicate that RPoly outperforms the SAT-based approach on most problem instances, being, in general, significantly more efficient

Towards compositional automated planning

The development of efficient propositional satisfiability problem solving algorithms (SAT solvers) in the past two decades has made automated planning using SAT-solvers\ua0an established AI planning approach. Modern SAT solvers can\ua0accommodate a wide variety of planning problems with a large number of variables. However, fast computing of reasonably long\ua0plans proves challenging for planning as satisfiability. In order to address this challenge, we present a compositional approach based on abstraction refinement that iteratively generates, solves and composes partial solutions from a parameterized planning problem. We show that this approach decomposes the monolithic planning problem into smaller problems and thus significantly speeds up plan calculation, at least for a class of tested planning problems