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Computational and Proof Complexity of Partial String Avoidability Itsykson, Dmitry Okhotin, Alexander Oparin, Vsevolod partial strings partial words avoidability proof complexity PSPACE-completeness 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Dmitry Itsykson and Alexander Okhotin and Vsevolod Oparin 2016 Is Part Of LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2016.51 urn:nbn:de:0030-drops-64637 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.51 eng https://creativecommons.org/licenses/by/3.0/legalcode