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DOI: 10.4230/LIPIcs.MFCS.2019.63
Computational Complexity of Synchronization under Regular Constraints

Authors: Henning Fernau, Vladimir V. Gusev, Stefan Hoffmann, Markus Holzer, Mikhail V. Volkov, and Petra Wolf

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract
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.
Cite as

Henning Fernau, Vladimir V. Gusev, Stefan Hoffmann, Markus Holzer, Mikhail V. Volkov, and Petra Wolf. Computational Complexity of Synchronization under Regular Constraints. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 63:1-63:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{fernau_et_al:LIPIcs.MFCS.2019.63,
  author =	{Fernau, Henning and Gusev, Vladimir V. and Hoffmann, Stefan and Holzer, Markus and Volkov, Mikhail V. and Wolf, Petra},
  title =	{{Computational Complexity of Synchronization under Regular Constraints}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{63:1--63:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.63},
  URN =		{urn:nbn:de:0030-drops-110078},
  doi =		{10.4230/LIPIcs.MFCS.2019.63},
  annote =	{Keywords: Finite automata, synchronization, computational complexity}
}
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