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On Limits of Symbolic Approach to SAT Solving

Authors Dmitry Itsykson , Sergei Ovcharov

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Author Details

Dmitry Itsykson
  • Ben-Gurion University of the Negev, Beer-Sheva, Israel
  • On leave from Steklov Institute of Mathematics at St. Petersburg, Russia
Sergei Ovcharov
  • St. Petersburg State University, Russia

Funding

  • Itsykson, Dmitry: Supported by European Research Council Grant No. 949707.

Cite As Get BibTex

Dmitry Itsykson and Sergei Ovcharov. On Limits of Symbolic Approach to SAT Solving. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 19:1-19:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SAT.2024.19

Abstract

We study the symbolic approach to the propositional satisfiability problem proposed by Aguirre and Vardi in 2001 based on OBDDs and symbolic quantifier elimination. We study the theoretical limitations of the most general version of this approach where it is allowed to dynamically change variable order in OBDD. We refer to algorithms based on this approach as OBDD(∧, ∃, reordering) algorithms. 
We prove the first exponential lower bound of OBDD(∧, ∃, reordering) algorithms on unsatisfiable formulas, and give an example of formulas having short tree-like resolution proofs that are exponentially hard for OBDD(∧, ∃, reordering) algorithms. We also present the first exponential lower bound for natural formulas with clear combinatorial meaning: every OBDD(∧, ∃, reordering) algorithm runs exponentially long on the binary pigeonhole principle BPHP^{n+1}_n.

Subject Classification

ACM Subject Classification
  • Theory of computation → Proof complexity
Keywords
  • Symbolic quantifier elimination
  • OBDD
  • lower bounds
  • tree-like resolution
  • proof complexity
  • error-correcting codes
  • binary pigeonhole principle

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References

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