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Origin-Equivalence of Two-Way Word Transducers Is in PSPACE Bose, Sougata Muscholl, Anca Penelle, Vincent Puppis, Gabriele Transducers origin semantics equivalence We consider equivalence and containment problems for word transductions. These problems are known to be undecidable when the transductions are relations between words realized by non-deterministic transducers, and become decidable when restricting to functions from words to words. Here we prove that decidability can be equally recovered the origin semantics, that was introduced by Bojanczyk in 2014. We prove that the equivalence and containment problems for two-way word transducers in the origin semantics are PSPACE-complete. We also consider a variant of the containment problem where two-way transducers are compared under the origin semantics, but in a more relaxed way, by allowing distortions of the origins. The possible distortions are described by means of a resynchronization relation. We propose MSO-definable resynchronizers and show that they preserve the decidability of the containment problem under resynchronizations. {} Schloss Dagstuhl – Leibniz-Zentrum für Informatik Sougata Bose and Anca Muscholl and Vincent Penelle and Gabriele Puppis 2018 Is Part Of LIPIcs, Volume 122, 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2018.22 urn:nbn:de:0030-drops-99213 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2018.22 eng https://creativecommons.org/licenses/by/3.0/legalcode