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  • We consider the following generalized notion of synchronization: A word is called a reset word of a subset of states of a deterministic finite automaton if it maps all states of the set to a unique state. It is known that the minimum length of such words is superpolynomial in worst cases, namely in a series of substantially nontransitive automata. We present a series of transitive binary automata with a strongly exponential minimum length. This also constitutes a progress in the research of composition sequences initiated by Arto Salomaa, because reset words of subsets are just a special case of composition sequences. Deciding about the existence of a reset word for given automaton and subset is known to be a PSPACE-complete problem, we prove that this holds even if we restrict the problem to transitive binary automata.
  • We consider the following generalized notion of synchronization: A word is called a reset word of a subset of states of a deterministic finite automaton if it maps all states of the set to a unique state. It is known that the minimum length of such words is superpolynomial in worst cases, namely in a series of substantially nontransitive automata. We present a series of transitive binary automata with a strongly exponential minimum length. This also constitutes a progress in the research of composition sequences initiated by Arto Salomaa, because reset words of subsets are just a special case of composition sequences. Deciding about the existence of a reset word for given automaton and subset is known to be a PSPACE-complete problem, we prove that this holds even if we restrict the problem to transitive binary automata. (en)
Title
  • Subset Synchronization of Transitive Automata
  • Subset Synchronization of Transitive Automata (en)
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  • Subset Synchronization of Transitive Automata
  • Subset Synchronization of Transitive Automata (en)
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  • RIV/00216208:11320/14:10281308!RIV15-GA0-11320___
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  • P(GA14-10799S)
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  • 48457
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  • RIV/00216208:11320/14:10281308
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  • Finite Automata; Composition Sequences; Reset Words; Synchronization (en)
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  • [F04E719F714E]
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  • Vorel, Vojtěch
http://bibframe.org/vocab/doi
  • 10.4204/EPTCS.151.26
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  • 11320
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