Prime clauses for fast enumeration of satisfying assignments to Boolean circuits

Abstract

Finding all satisfying assignments of a propositional formula has many applications in the design of hardware and software. An approach to this problem augments a clause-recording propositional satisfiability solver with the ability to add blocking clauses, which prevent the solver from visiting the same solution more than once. One generates a blocking clause from a satisfying assignment by taking its complement. In this paper, we present an improved algorithm for finding all satisfying assignments for a generic Boolean circuit. An optimization based on lifting-which generates minimal satisfying assignments-yields prime blocking clauses. Thanks to the primality of the blocking clauses, the derived conflict clauses usually prune both satisfiable and unsatisfiable points at once. The efficiency of our new algorithm is demonstrated by our preliminary results on SAT-based unbounded model checking.

Complementary Synthesis for Encoder with Flow Control Mechanism

“…In Ravi and Somenzi [2004] and Chauhan et al [2004], those variables whose absence can't make obj ≡ 0 satisfiable are removed one by one. In Shen et al [2005] and Jin and Somenzi [2005], conflict-analysis-based approaches are used to remove multiple irrelevant variables in one SAT run. In Grumberg et al [2004], the variable set is divided into an important subset and an unimportant subset.…”