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Evaluating the Hardness of SAT Instances Using Evolutionary Optimization Algorithms

Authors Alexander Semenov, Daniil Chivilikhin, Artem Pavlenko, Ilya Otpuschennikov, Vladimir Ulyantsev, Alexey Ignatiev

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Alexander Semenov
  • ITMO University, St. Petersburg, Russia
Daniil Chivilikhin
  • ITMO University, St. Petersburg, Russia
Artem Pavlenko
  • ITMO University, St. Petersburg, Russia
  • JetBrains Research, St. Petersburg, Russia
Ilya Otpuschennikov
  • ISDCT SB RAS, Irkutsk, Russia
Vladimir Ulyantsev
  • ITMO University, St. Petersburg, Russia
Alexey Ignatiev
  • Monash University, Melbourne, Australia

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Alexander Semenov, Daniil Chivilikhin, Artem Pavlenko, Ilya Otpuschennikov, Vladimir Ulyantsev, and Alexey Ignatiev. Evaluating the Hardness of SAT Instances Using Evolutionary Optimization Algorithms. In 27th International Conference on Principles and Practice of Constraint Programming (CP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 210, pp. 47:1-47:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


Propositional satisfiability (SAT) solvers are deemed to be among the most efficient reasoners, which have been successfully used in a wide range of practical applications. As this contrasts the well-known NP-completeness of SAT, a number of attempts have been made in the recent past to assess the hardness of propositional formulas in conjunctive normal form (CNF). The present paper proposes a CNF formula hardness measure which is close in conceptual meaning to the one based on Backdoor set notion: in both cases some subset B of variables in a CNF formula is used to define the hardness of the formula w.r.t. this set. In contrast to the backdoor measure, the new measure does not demand the polynomial decidability of CNF formulas obtained when substituting assignments of variables from B to the original formula. To estimate this measure the paper suggests an adaptive (ε,δ)-approximation probabilistic algorithm. The problem of looking for the subset of variables which provides the minimal hardness value is reduced to optimization of a pseudo-Boolean black-box function. We apply evolutionary algorithms to this problem and demonstrate applicability of proposed notions and techniques to tests from several families of unsatisfiable CNF formulas.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automated reasoning
  • Hardware → Theorem proving and SAT solving
  • Theory of computation → Optimization with randomized search heuristics
  • Mathematics of computing → Combinatorial optimization
  • SAT solving
  • Boolean formula hardness
  • Backdoors
  • Evolutionary algorithms


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