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Computational Complexity of Synchronization under Regular Constraints Fernau, Henning Gusev, Vladimir V. Hoffmann, Stefan Holzer, Markus Volkov, Mikhail V. Wolf, Petra Finite automata synchronization computational complexity Many variations of synchronization of finite automata have been studied in the previous decades. Here, we suggest studying the question if synchronizing words exist that belong to some fixed constraint language, given by some partial finite automaton called constraint automaton. We show that this synchronization problem becomes PSPACE-complete even for some constraint automata with two states and a ternary alphabet. In addition, we characterize constraint automata with arbitrarily many states for which the constrained synchronization problem is polynomial-time solvable. We classify the complexity of the constrained synchronization problem for constraint automata with two states and two or three letters completely and lift those results to larger classes of finite automata. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Henning Fernau and Vladimir V. Gusev and Stefan Hoffmann and Markus Holzer and Mikhail V. Volkov and Petra Wolf 2019 Is Part Of LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2019.63 urn:nbn:de:0030-drops-110078 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.63 eng https://creativecommons.org/licenses/by/3.0/legalcode