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We describe an incremental algorithm for computing inter-polants for a pair ϕA, ϕB of formulas in propositional logic. In contrast with the common approaches, our method does not require a proof of unsatisfiability of ϕA ∧ ϕB, and can be realized using any SAT solver as a black box. We achieve this by combining model enumeration with the ability to easily(More)
—Formal verification is a reliable and fully automatic technique for proving correctness of hardware designs. Its main drawback is the high complexity of verification , and this problem is especially acute in regression verification, where a new version of the design, differing from the previous version very slightly, is verified with respect to the same or(More)
Constrained sampling and counting are two fundamental problems arising in domains ranging from artificial intelligence and security, to hardware and software testing. Recent approaches to approximate solutions for these problems rely on employing SAT solvers and universal hash functions that are typically encoded as XOR constraints of length n/2 for an(More)
We study the problem of encoding cardinality constraints (threshold functions) on Boolean variables into CNF. Specifically, we propose new encod-ings based on (perfect) hashing that are efficient in terms of the number of clauses, auxiliary variables, and propagation strength. We compare the properties of our encodings to known ones, and provide(More)
In this paper we address the following problem: given an unsatisfi-able CNF formula F, find a minimal subset of variables of F that constitutes the set of variables in some unsatisfiable core of F. This problem, known as variable MUS (VMUS) computation problem, captures the need to reduce the number of variables that appear in unsatisfiable cores. Previous(More)
Halpern and Pearl introduced a definition of actual causal-ity; Eiter and Lukasiewicz showed that computing whether X = x is a cause of Y = y is NP-complete in binary models (where all variables can take on only two values) and Σ P 2-complete in general models. In the final version of their paper , Halpern and Pearl slightly modified the definition of(More)
Constrained sampling and counting are two fundamental problems in artificial intelligence with a diverse range of applications , spanning probabilistic reasoning and planning to constrained-random verification. While the theory of these problems was thoroughly investigated in the 1980s, prior work either did not scale to industrial size instances or gave up(More)