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Theses

Exploitation of dynamic symmetries for solving SAT problems

Abstract : Boolean satisfiability (SAT) solves the problem of finding a solution to a propositional Boolean formula. This NP-complete problem can model a wide variety of industrial and academic problems covering planning, formal verification, logic optimization... Many systems in practice exhibit symmetries, that can allow to reason on a quotient abstraction of the search space that can be exponentially smaller than the full search space in favorable cases. In this thesis, we explore how to exploit symmetry to improve the performance of SAT solvers. Existing approaches to exploit symmetries in SAT solving, consist in computing the symmetries of the problem then generating so-called static "symmetry breaking predicates" (sbps) that are added to the problem, forcing the solver to adopt only one representative for each equivalence class. The problem with this approach is that the number of additional constraints can be larger than the original system, and may overload the solver. The first contribution of this thesis called CDCL[sym] is a novel lightweight and dynamic algorithm, that only introduces these additional sbps opportunistically as the solver progresses. A second approach to exploit symmetries consists in so-called dynamic symmetry breaking that is concerned with symmetric propagation of the deductions of the solver when possible. This approach solves some models that static symmetry breaking cannot solve, and vice-versa. In our second contribution of this thesis, we combine this strategy with the previous approach, enabling for the first time on the fly propagation of symmetric deductions while still gaining the benefits of CDCL[sym].
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  • HAL Id : tel-03128926, version 1

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Hakan Metin. Exploitation of dynamic symmetries for solving SAT problems. Performance [cs.PF]. Sorbonne Université, 2019. English. ⟨NNT : 2019SORUS552⟩. ⟨tel-03128926⟩

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