Exploiting Resolution-based Representations for MaxSAT Solving

Most recent MaxSAT algorithms rely on a succession of calls to a SAT solver in order to find an optimal solution. In particular, several algorithms take advantage of the ability of SAT solvers to identify unsatisfiable subformulas. Usually, these MaxSAT algorithms perform better when small unsatisfiable subformulas are found early. However, this is not the case in many problem instances, since the whole formula is given to the SAT solver in each call. In this paper, we propose to partition the MaxSAT formula using a resolution-based graph representation. Partitions are then iteratively joined by using a proximity measure extracted from the graph representation of the formula. The algorithm ends when only one partition remains and the optimal solution is found. Experimental results show that this new approach further enhances a state of the art MaxSAT solver to optimally solve a larger set of industrial problem instances

Approximation Strategies for Incomplete MaxSAT

Incomplete MaxSAT solving aims to quickly find a solution that attempts to minimize the sum of the weights of the unsati sfied soft clauses without providing any optimality guarantees. In th is paper, we propose two approximation strategies for improving incomp lete MaxSAT solving. In one of the strategies, we cluster the weights and approximate them with a representative weight. In another strategy, we b reak up the problem of minimizing the sum of weights of unsatisfiable clauses into multiple minimization subproblems. Experimental res ults show that approximation strategies can be used to find better solution s than the best incomplete solvers in the MaxSAT Evaluation 2017

Approximation Strategies for Incomplete MaxSAT

Incomplete MaxSAT solving aims to quickly find a solution that attempts to minimize the sum of the weights of the unsatisfied soft clauses without providing any optimality guarantees. In this paper, we propose two approximation strategies for improving incomplete MaxSAT solving. In one of the strategies, we cluster the weights and approximate them with a representative weight. In another strategy, we break up the problem of minimizing the sum of weights of unsatisfiable clauses into multiple minimization subproblems. Experimental results show that approximation strategies can be used to find better solutions than the best incomplete solvers in the MaxSAT Evaluation 2017.Comment: 10 pages, 3 algorithms, 1 figure, International Conference on Principles and Practice of Constraint Programming (CP) 201

On Tackling the Limits of Resolution in SAT Solving

The practical success of Boolean Satisfiability (SAT) solvers stems from the CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a propositional proof complexity perspective, CDCL is no more powerful than the resolution proof system, for which many hard examples exist. This paper proposes a new problem transformation, which enables reducing the decision problem for formulas in conjunctive normal form (CNF) to the problem of solving maximum satisfiability over Horn formulas. Given the new transformation, the paper proves a polynomial bound on the number of MaxSAT resolution steps for pigeonhole formulas. This result is in clear contrast with earlier results on the length of proofs of MaxSAT resolution for pigeonhole formulas. The paper also establishes the same polynomial bound in the case of modern core-guided MaxSAT solvers. Experimental results, obtained on CNF formulas known to be hard for CDCL SAT solvers, show that these can be efficiently solved with modern MaxSAT solvers

A Hybrid Approach to Optimization in Answer Set Programming

Peer reviewe

Subsumed Label Elimination for Maximum Satisfiability

Proceeding volume: 285Peer reviewe

Boosting Answer Set Optimization with Weighted Comparator Networks

Answer set programming (ASP) is a paradigm for modeling knowledge intensive domains and solving challenging reasoning problems. In ASP solving, a typical strategy is to preprocess problem instances by rewriting complex rules into simpler ones. Normalization is a rewriting process that removes extended rule types altogether in favor of normal rules. Recently, such techniques led to optimization rewriting in ASP, where the goal is to boost answer set optimization by refactoring the optimization criteria of interest. In this paper, we present a novel, general, and effective technique for optimization rewriting based on comparator networks, which are specific kinds of circuits for reordering the elements of vectors. The idea is to connect an ASP encoding of a comparator network to the literals being optimized and to redistribute the weights of these literals over the structure of the network. The encoding captures information about the weight of an answer set in auxiliary atoms in a structured way that is proven to yield exponential improvements during branch-and-bound optimization on an infinite family of example programs. The used comparator network can be tuned freely, e.g., to find the best size for a given benchmark class. Experiments show accelerated optimization performance on several benchmark problems.Comment: 36 page

MaxSAT Evaluation 2021 : Solver and Benchmark Descriptions

Non peer reviewe