Computer Science > Computational Complexity
[Submitted on 4 Mar 2020 (v1), last revised 11 May 2020 (this version, v2)]
Title:Towards a Complexity-theoretic Understanding of Restarts in SAT solvers
View PDFAbstract:Restarts are a widely-used class of techniques integral to the efficiency of Conflict-Driven Clause Learning (CDCL) Boolean SAT solvers. While the utility of such policies has been well-established empirically, a theoretical explanation of whether restarts are indeed crucial to the power of CDCL solvers is lacking. In this paper, we prove a series of theoretical results that characterize the power of restarts for various models of SAT solvers. More precisely, we make the following contributions. First, we prove an exponential separation between a {\it drunk} randomized CDCL solver model with restarts and the same model without restarts using a family of satisfiable instances. Second, we show that the configuration of CDCL solver with VSIDS branching and restarts (with activities erased after restarts) is exponentially more powerful than the same configuration without restarts for a family of unsatisfiable instances. To the best of our knowledge, these are the first separation results involving restarts in the context of SAT solvers. Third, we show that restarts do not add any proof complexity-theoretic power vis-a-vis a number of models of CDCL and DPLL solvers with non-deterministic static variable and value selection.
Submission history
From: Chunxiao Li [view email][v1] Wed, 4 Mar 2020 20:30:04 UTC (245 KB)
[v2] Mon, 11 May 2020 17:33:20 UTC (235 KB)
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