Balancing Scalability and Uniformity in SAT Witness Generator

Abstract

Constrained-random simulation is the predominant approach used in the industry for functional verification of complex digital designs. The effectiveness of this approach depends on two key factors: the quality of constraints used to generate test vectors, and the randomness of solutions generated from a given set of constraints. In this paper, we focus on the second problem, and present an algorithm that significantly improves the state-of-the-art of (almost-)uniform generation of solutions of large Boolean constraints. Our algorithm provides strong theoretical guarantees on the uniformity of generated solutions and scales to problems involving hundreds of thousands of variables.

On Parallel Scalable Uniform SAT Witness Generation

“…This has been observed repeatedly in the literature [6] and by industry practitioners 4 . In this paper, we take a step towards remedying the current situation by proposing an easily parallelizable sampling algorithm for Boolean constraints that provides strong theoretical guarantees (similar to those provided by an almost-uniform generator) in the context of CRV, and also runs significantly faster than current state-of-the-art techniques on a diverse set of benchmark problems.…”

“…Our algorithm, named UniGen2, bears some structural similarities with the UniGen algorithm proposed earlier in [6]. Nevertheless, there are key differences that allow UniGen2 to outperform UniGen significantly.…”

“…For the rest of the paper, we use S to denote the sampling set, the set of variables onto which we desire assignments to be projected. Even when no projection is desired, S can often be restricted to a very small subset of X (an independent support; see [6] for details) such that R F ∼ = R F ↓S . For notational simplicity, we omit mentioning F and S when they are clear from the context.…”

“…Recently, several random hashing-based techniques have been proposed to bridge the wide gap between scalable algorithms and those that give strong guarantees of uniformity when sampling witnesses of propositional constraints [4,6,9]. Hashing-based sampling techniques were originally pioneered by Sipser [23] and further used by Jerrum, Valiant, and Vazirani [15], and Bellare, Goldreich, and Petrank [2].…”

“…Under an appropriate partitioning scheme, choosing a random witness from a randomly chosen cell provides strong uniformity guarantees. The most recent instance of this approach is called UniGen [6]. While UniGen scales to formulae much larger than those that can be handled by previous state-of-the-art techniques, the runtime performance of UniGen still falls short of industry requirements.…”