The notion of synchronization of finite automata is connected to one of the long-standing open problems in combinatorial automata theory, which is Černý’s Conjecture. In this paper, we focus on so-called synchronization games. We will discuss how to present synchronization questions in a playful way. This leads us to study related complexity questions on certain classes of finite automata. More precisely, we consider weakly acyclic, commutative and k-simple idempotent automata. We encounter a number of complexity classes, ranging from L up to PSPACE.
@InProceedings{fernau_et_al:LIPIcs.FUN.2022.14, author = {Fernau, Henning and Haase, Carolina and Hoffmann, Stefan}, title = {{The Synchronization Game on Subclasses of Automata}}, booktitle = {11th International Conference on Fun with Algorithms (FUN 2022)}, pages = {14:1--14:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-232-7}, ISSN = {1868-8969}, year = {2022}, volume = {226}, editor = {Fraigniaud, Pierre and Uno, Yushi}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2022.14}, URN = {urn:nbn:de:0030-drops-159842}, doi = {10.4230/LIPIcs.FUN.2022.14}, annote = {Keywords: Synchronization of finite automata, computational complexity} }
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