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Resolution Lower Bounds for Refutation Statements

Author Michal Garlík

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Author Details

Michal Garlík
  • Dept. Ciències de la Computació, Universitat Politècnica de Catalunya, C. Jordi Girona, 1-3, 08034 Barcelona, Spain

Funding

Funded by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant agreement ERC-2014-CoG 648276 (AUTAR).

Cite AsGet BibTex

Michal Garlík. Resolution Lower Bounds for Refutation Statements. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 37:1-37:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.MFCS.2019.37

Abstract

For any unsatisfiable CNF formula we give an exponential lower bound on the size of resolution refutations of a propositional statement that the formula has a resolution refutation. We describe three applications. (1) An open question in [Atserias and Müller, 2019] asks whether a certain natural propositional encoding of the above statement is hard for Resolution. We answer by giving an exponential size lower bound. (2) We show exponential resolution size lower bounds for reflection principles, thereby improving a result in [Albert Atserias and María Luisa Bonet, 2004]. (3) We provide new examples of CNFs that exponentially separate Res(2) from Resolution (an exponential separation of these two proof systems was originally proved in [Nathan Segerlind et al., 2004]).

Subject Classification

ACM Subject Classification
  • Theory of computation → Proof complexity
Keywords
  • reflection principles
  • refutation statements
  • Resolution
  • proof complexity

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References

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