Computational and proof complexity of partial string avoidability

Research output

Abstract

The partial string avoidability problem, also known as partial word avoidability, is stated as follows: Given a finite set of strings with possible "holes" (undefined symbols), determine whether there exists any two-sided infinite string containing no substrings from this set, assuming that a hole matches every symbol. The problem is known to be NP-hard and in PSPACE, and this paper establishes its PSPACE-completeness. Next, string avoidability over the binary alphabet is interpreted as a version of conjunctive normal form (CNF) satisfiability problem (SAT), with each clause having infinitely many shifted variants. Non-satisfiability of these formulas can be proved using variants of classical propositional proof systems, augmented with derivation rules for shifting constraints (such as clauses, inequalities, polynomials, etc). Two results on their proof complexity are established. First, there is a particular formula that has a short refutation in Resolution with shift, but requires classical proofs of exponential size (Resolution, Cutting Plane, Polynomial Calculus, etc.). At the same time, exponential lower bounds for shifted versions of classical proof systems are established.

Original languageEnglish
Title of host publication41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016
EditorsAnca Muscholl, Piotr Faliszewski, Rolf Niedermeier
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770163
DOIs
Publication statusPublished - 1 Aug 2016
Event41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 - Krakow
Duration: 22 Aug 201626 Aug 2016

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume58
ISSN (Print)1868-8969

Conference

Conference41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016
CountryPoland
CityKrakow
Period22/08/1626/08/16

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Scopus subject areas

  • Software

Cite this

Itsykson, D., Okhotin, A., & Oparin, V. (2016). Computational and proof complexity of partial string avoidability. In A. Muscholl, P. Faliszewski, & R. Niedermeier (Eds.), 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 [51] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 58). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.MFCS.2016.51