An incremental algorithm to check satisfiability for bounded model checking

lengths is translated into a sequence of satisfiability (SAT) checks. It is natural to try to exploit the similarity of these SAT instances by forwarding clauses learned during conflict analysis from one instance to the next. The methods proposed to identify clauses that remain valid fall into two categories: Those that are oblivious to the mechanism that generates the sequence of SAT instances and those that rely on it. In the case of a BMC run, it was observed by Strichman [20] that those clauses learned during one SAT check that only depend on the structure of the model remain valid when checking for longer counterexamples. Eén and Sörensson [9] pointed out that all learned clauses can be forwarded if the translation into SAT obeys commonly followed rules. Many clauses that are forwarded this way, however, are of little usefulness and may degrade performance. This paper presents an extension to Strichman’s approach in the form of a more general criterion to filter conflict clauses that can be profitably forwarded to successive instances. This criterion, in particular, is still syntactic and quite efficient, but accounts for the presence of both primary and auxiliary objectives in the SAT instance. This pape

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.

CirCUs: A Satisfiability Solver Geared towards Bounded Model Checking

Abstract. CirCUs is a satisfiability solver that works on a combination of And-Inverter-Graph, CNF clauses, and BDDs. It has been designed to work well with bounded model checking. It takes as inputs a Boolean circuit (e.g., the model unrolled k times) and an optional set of additional constraints (for instance, requesting that a solution correspond to a simple path) in the form of CNF clauses or BDDs. The algorithms in CirCUs take advantage of the mixed representation by applying powerful BDD-based implication algorithms, and decision heuristics that are objective-driven. CirCUs supports incremental SAT solving, early termination checks, and other analyses of the model that translate into SAT. Experimental results demonstrate CirCUs’s efficiency

Disequality Management in Integer Difference Logic via Finite Instantiations ∗

The last few years have seen the advent of a new breed of decision procedures for various fragments of first-order logic based on propositional abstraction. A lazy satisfiability checker for a given fragment of first-order logic invokes a theory-specific decision procedure (a theory solver) on a (partial) model for the abstraction. If the model is found to be consistent in the given theory, then a model for the original formula has been found. Otherwise, a refinement of the propositional abstraction is extracted from the proof of inconsistency and the search is resumed. We describe a theory solver for integer difference logic that is effective when the formula to be decided contains equality and disequality (negated equality) constraints so that the decision problem partakes of the nature of the pigeonhole problem. We propose a reduction of the problem to propositional satisfiability by computing bounds on a sufficient subset of solutions, and present experimental evidence for the efficiency of this approach