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.

Checking Safety by Inductive Generalization of Counterexamples to Induction

“…This minimal subclause d is known as a prime implicate [5], [6]. There can be exponentially many such minimal subclauses, yet there may not be any prime implicate if ϕ ⇒ c. Section IV-B presents an optimal implementation of implicate.…”

On automated trigger event generation in post-silicon validation

“…The task given in Step 2 can be formulated as an AllSAT problem, which is to find all input assignments of a boolean satisfiability (SAT) problem that will satisfy all the specified constraints [8]. This can be done by formulating the boolean relationships of the isolated part of the circuit as a SAT instance with the available trigger signals as input variables, and the targeted trigger event as additional constraints in the SAT problem.…”

Solving satisfiability problems with preferences

“…Other works which exploit further techniques to eliminate previously computed solutions in SAT include, e.g., [23][24][25] in the context of symbolic model checking [26]. However, the framework used in [10] assumes a consistent set of preferences, does not allow for ordering the preferences and ultimately has a different semantics.…”

“…In particular, (1)(2)(3)(4)(5) are Formal Verification instances ((1-2) from the Bejing'96 competition, (3)(4)(5) by Ofer Shtrichman); (6)(7)(8)(9)(10)(11)(12)(13)(14) are planning problems from SATPLAN; (15)(16)(17)(18)(19)(20) are Data Encryption Standard instances; (21)(22)(23)(24)(25)(26) are quasi group instances. The domains contain, in general, more benchmarks that the one we show: The instances showed representative of the 9 A literal l is pure in a set of clauses ϕ if l does not belong to any clause in ϕ.…”