CirCUs: A Hybrid Satisfiability Solver

Abstract

CirCUs is a satisfiability solver that works on a combination of an And-Inverter-Graph (AIG), Conjunctive Normal Form (CNF) clauses, and Binary Decision Diagrams (BDDs). We show how BDDs are used by CirCUs to help in the solution of SAT instances given in CNF. Specifically, the clauses are sorted by solving a hypergraph linear arrangement problem. Then they are clustered by an algorithm that strives to avoid explosion in the resulting BDD sizes. If clustering results in a single diagram, the SAT instance is solved directly. Otherwise, search for a satisfying assignment is conducted on the original clauses, enhanced with information extracted from the BDDs. We also describe a new decision variable selection heuristic that is based on recognizing that the variables involved in a conflict clause are often best treated as a related group. We present experimental results that demonstrate Cir-CUs's efficiency especially for medium-size SAT instances that are hard to solve by traditional solvers based on DPLL.

Extended Resolution Proofs for Conjoining BDDs

“…Using BDDs for SAT is an active research area [15][16][17][18][19][20]. It turns out that BDD [21] and search based techniques [2] are complementary [22,23].…”

“…There are instances for which one works better than the other. Therefore, combinations have been proposed [16,17,20] to obtain the benefits of both, usually in the form of using BDDs for preprocessing. However, in all these approaches where BDDs have been used, proof generation has not been possible so far.…”

“…Therefore our solver is far less powerful than more sophisticated BDD-based SAT solvers [15][16][17][18][19][20]. In particular, we currently cannot handle existential quantification.…”

Fifty-Five Solvers in Vancouver: The SAT 2004 Competition

“…brchaff (R. Bruni), circush0, circush1 (H. Jin) [9], cls (W. Ruml) [6], satzilla, satzilla-nr, satzilla-r (E. Nudelman)…”

A View from the Engine Room: Computational Support for Symbolic Model Checking

“…While DPLL works well on many problems, it has severe weaknesses, some of which can be filled by more "niche" approaches, such as OBDDs. Some attempts have been made to develop SAT solvers that use different combinations of DPLL and OBDDs, e.g., [7], but none of these has demonstrated consistent improvements over DPLL. In particular, it seems like the main advantage of current DPLL/OBDD hybrids is that they can solve problems that are tractable using either DPLL or OBDDs.…”