When Boolean Satisfiability Meets Gaussian Elimination in a Simplex Way
نویسندگان
چکیده
Recent research on Boolean satisfiability (SAT) reveals modern solvers’ inability to handle formulae in the abundance of parity (xor) constraints. Although xor-handling in SAT solving has attracted much attention, challenges remain to completely deduce xor-inferred implications and conflicts, to effectively reduce expensive overhead, and to directly generate compact interpolants. This paper integrates SAT solving tightly with Gaussian elimination in the style of Dantzig’s simplex method. It yields a powerful tool overcoming these challenges. Experiments show promising performance improvements and efficient derivation of compact interpolants, which are otherwise unobtainable.
منابع مشابه
Intersection-Based Methods for Satisfiability Using Boolean Rings
A potential advantage of using a Boolean-ring formalism for propositional formulæ is the large measure of simplification it facilitates. We propose a combined linear and binomial representation for Boolean ring polynomials, with which one can easily apply Gaussian elimination and Horn-clause methods to advantage. The framework is especially amenable to intersection-based learning. Experiments s...
متن کاملBoolean Rings for Intersection-Based Satisfiability
A potential advantage of using a Boolean-ring formalism for propositional formulæ is the large measure of simplification it facilitates. We propose a combined linear and binomial representation for Booleanring polynomials with which one can easily apply Gaussian elimination and Horn-clause methods to advantage. We demonstrate that this framework, with its enhanced simplification, is especially ...
متن کاملSimulating Parity Reasoning (extended version)
Propositional satisfiability (SAT) solvers, which typically operate using conjunctive normal form (CNF), have been successfully applied in many domains. However, in some application areas such as circuit verification, bounded model checking, and logical cryptanalysis, instances can have many parity (xor) constraints which may not be handled efficiently if translated to CNF. Thus, extensions to ...
متن کاملConstraint Propagation as a Proof System
Refutation proofs can be viewed as a special case of constraint propagation, which is a fundamental technique in solving constraint-satisfaction problems. The generalization lifts, in a uniform way, the concept of refutation from Boolean satisfiability problems to general constraint-satisfaction problems. On the one hand, this enables us to study and characterize basic concepts, such as refutat...
متن کاملExtending Sat Solver with Parity Constraints
Current methods for solving Boolean satisfiability problem (SAT) are scalable enough to solve discrete nonlinear problems involving hundreds of thousands of variables. However, modern SAT solvers scale poorly with problems involving parity constraints (linear equations modulo 2). Gaussian elimination can be used to solve a system of linear equation effectively but it cannot be applied as such w...
متن کامل