Comparison of PBO solvers in a dependency solving domain

Linux package managers have to deal with dependencies and conflicts of packages required to be installed by the user. As an NP-complete problem, this is a hard task to solve. In this context, several approaches have been pursued. Apt-pbo is a package manager based on the apt project that encodes the dependency solving problem as a pseudo-Boolean optimization (PBO) problem. This paper compares different PBO solvers and their effectiveness on solving the dependency solving problem.Comment: In Proceedings LoCoCo 2010, arXiv:1007.083

Ario: A Linear Integer Arithmetic Logic Solver

Abstract — In this paper we describe our solver for systems of linear integer arithmetic logic. Such systems are commonly used in design verification applications and are classified under Satisfiability Modulo Theories (SMT) problems. Recognizing the fact that in many such applications the majority of atoms are equalities or integer unit-two-variable inequalities (UTVPIs), we present a framework that integrates specialized theory solvers for those atoms within a SAT solver. The unique feature of our strategy is its simultaneous adoption of both a congruence-closure equality solver and a transitive-closure UTVPI solver to find a satisfiable set of those atoms. A full-scale ILP solver is then utilized to check the consistency of all integer constraints within the solution. Other notable features of our solver include its combined deduction and learning schemes that collectively make our solver distinct among similar solvers. I

Pueblo: A modern pseudo-boolean sat solver

In this report we introduce a new SAT solver that integrates logic-based reasoning and integer programming meth-ods to systems of CNF and PB constraints. Its novel features include an efficient PB literal watching strategy that takes advantage of the preponderance of unit-coefficient literals in most PB constraints. Additionally, the solver incorporates several PB learning methods that take advantage of the pruning power of PB constraints while mini-mizing their overhead. Empirical evidence suggests that such judicious injection of IP techniques can be quite effec-tive in practice. CSE-TR-492-04: Pueblo: A Modern Pseudo-Boolean SAT Solver 2

Pueblo: A hybrid pseudo-boolean SAT solver

This paper introduces a new hybrid method for efficiently integrating Pseudo-Boolean (PB) constraints into generic SAT solvers in order to solve PB satisfiability and optimization problems. To achieve this, we adopt the cutting-plane technique to draw inferences among PB constraints and combine it with generic implication graph analysis for conflictinduced learning. Novel features of our approach include a light-weight and efficient hybrid learning and backjumping strategy for analyzing PB constraints and CNF clauses in order to simultaneously learn both a CNF clause and a PB constraint with minimum overhead and use both to determine the backtrack level. Several techniques for handling the original and learned PB constraints are introduced. Overall, our method benefits significantly from the pruning power of the learned PB constraints, while keeping the overhead of adding them into the problem low. In this paper, we also address two other methods for solving PB problems, namely Integer Linear Programming (ILP) and pre-processing to CNF SAT, and present a thorough comparison between them and our hybrid method. Experimental comparison of our method against other hybrid approaches is also demonstrated. Additionally, we provide details of the MiniSAT-based implementation of our solver Pueblo to enable the reader to construct a similar one

A scalable method for solving satisfiability of integer linear arithmetic logic

Abstract. In this paper, we present a hybrid method for deciding problems involving integer and Boolean variables which is based on generic SAT solving techniques augmented with a) a polynomial-time ILP solver for the special class of Unit-Two-Variable-Per-Inequality (unit TVPI or UTVPI) constraints and b) an independent solver for general integer linear constraints. In our approach, we present a novel method for encoding linear constraints into the SAT solver through binary “indicator” variables. The hybrid SAT problem is subsequently solved using a SAT search procedure in close collaboration with the UTVPI solver. The UTVPI solver interacts closely with the Boolean SAT solver by passing implications and conflicting assignments. The non-UTV-PI constraints are handled separately and participate in the learning scheme of the SAT solver through an innovative method based on the theory of cutting planes. Empirical evidence on software verification benchmarks is presented that demonstrates the advantages of ou