Enhancing Reasoning with the Extension Rule in CDCL SAT Solvers

EasyChair Preprint 2121

Abstract

The extension rule first introduced by G. Tseitin is a simple but powerful rule that, when added to resolution, leads to an exponentially stronger proof system known as extended resolution(ER). Despite the outstanding theoretical results obtained with ER, its exploitation in practice to improve SAT solvers' efficiency still poses some challenging issues. There have been several attempts in the literature aiming at integrating the extension rule within CDCL SAT solvers but the results are in general not as promising as in theory. An important remark that can be made on these attempts is that most of them focus on reducing the sizes of the proofs using the extended variables introduced in the solver. We adopt in this work a different view. We see extended variables as a means to enhance reasoning in solvers and therefore to give them the ability of reasoning on various semantic aspects of variables. Experiments carried out on the 2018 SAT competition's benchmarks show the use of the extension rule in CDCL SAT solvers to be practically useful for both satisfiable and unsatisfiable instances.

Keyphrases: CDCL, Extension Rule, SAT

@booklet{EasyChair:2121,
  author    = {Rodrigue Konan Tchinda and Clémentin Tayou Djamegni},
  title     = {Enhancing Reasoning with the Extension Rule in CDCL SAT Solvers},
  howpublished = {EasyChair Preprint 2121},
  year      = {EasyChair, 2019}}