Recognizing synchronizing automata with finitely many minimal synchronizing words is PSPACE-complete

Authors:
Elena V. Pribavkina;Emanuele Rodaro
Affiliations:
Ural State University, Ekaterinburg, Russia;Centro de Matematica, Faculdade de Ciências, Universidade do Porto, Porto, Portugal
Venue:
CiE'11 Proceedings of the 7th conference on Models of computation in context: computability in Europe
Year:
2011

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Synchronizing automata with finitely many minimal synchronizing words

Information and Computation

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Abstract

A deterministic finite-state automaton A is said to be synchronizing if there is a synchronizing word, i.e. a word that takes all the states of the automaton A to a particular one. We consider synchronizing automata whose language of synchronizing words is finitely generated as a two-sided ideal in Σ*. Answering a question stated in [1], here we prove that recognizing such automata is a PSPACE-complete problem.