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Finding all satisfying assignments of a propositional formula has many applications to the synthesis and verification of hardware and software. An approach to this problem that has recently emerged augments a clause-recording propositional satisfiability solver with the ability to add "blocking clauses." One generates a blocking clause from a satisfying assignment by taking its complement. The resulting clause prevents the solver from visiting the same solution again. Every time a blocking clause is added the search is resumed until the instance becomes unsatisfiable. Various optimization techniques are applied to get smaller blocking clauses, since enumerating each satisfying assignment would be very inefficient. In this paper, we present an improved algorithm for finding all satisfying assignments for a generic Boolean circuit. Our work is based on a hybrid SAT solver that can apply conflict analysis and implications to both CNF formulae and general circuits. Thanks to this capability, reduction of the blocking clauses can be efficiently performed without altering the solver's state (e.g., its decision stack). This reduces the overhead incurred in resuming the search. Our algorithm performs conflict analysis on the blocking clause to derive a proper conflict clause for the modified formula. Besides yielding a valid, nontrivial backtracking level, the derived conflict clause is usually more effective at pruning the search space, since it may encompass both satisfiable and unsatisfiable points. Another advantage is that the derived conflict clause provides more flexibility in guiding the score-based heuristics that select the decision variables. The efficiency of our new algorithm is demonstrated by our preliminary results on SAT-based unbounded model checking of VIS benchmark models. Work supported in part by SRC contract 2004-TJ-920.

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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.

In Bounded Model Checking (BMC), the search for counterexamples of increasing 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 paper also introduces a technique to distill clauses to be forwarded even though they fail the syntactic check. Distillation is a semantic approach that can be applied in general to incremental SAT, and often produces clauses that are independent of the primary objective, and hence remain valid for the remainder of the sequence of instances. In addition, distillation often improves the quality of the clauses, that is, their ability to prevent the examination of large regions of the search space. Experimental results obtained with the CirCUs SAT solver confirm the efficacy of the proposed techniques, especially for large, hard problems.