Clausal Proofs for Pseudo-Boolean Reasoning

Abstract

AbstractWhen augmented with a Pseudo-Boolean (PB) solver, a Boolean satisfiability (SAT) solver can apply apply powerful reasoning methods to determine when a set of parity or cardinality constraints, extracted from the clauses of the input formula, has no solution. By converting the intermediate constraints generated by the PB solver into ordered binary decision diagrams (BDDs), a proof-generating, BDD-based SAT solver can then produce a clausal proof that the input formula is unsatisfiable. Working together, the two solvers can generate proofs of unsatisfiability for problems that are intractable for other proof-generating SAT solvers. The PB solver can, at times, detect that the proof can exploit modular arithmetic to give smaller BDD representations and therefore shorter proofs.