Vojtěch Vorel (Charles University in Prague) |

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. |

Research supported by the Czech Science Foundation grant GA14-10799S.

Published: 21st May 2014.

ArXived at: http://dx.doi.org/10.4204/EPTCS.151.26 | bibtex | |

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