Automata with Extremal Minimality Conditions

  • Antonio Restivo
  • Roberto Vaglica
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6224)


It is well known that the minimality of a deterministic finite automaton (DFA) depends on the set of final states. In this paper we study the minimality of a strongly connected DFA by varying the set of final states. We consider, in particular, some extremal cases. A strongly connected DFA is called uniformly minimal if it is minimal, for any choice of the set of final states. It is called never-minimal if it is not minimal, for any choice of the set of final states. We show that there exists an infinite family of uniformly minimal automata and that there exists an infinite family of never-minimal automata. Some properties of these automata are investigated and, in particular, we consider the complexity of the problem to decide whether an automaton is uniformly minimal or never-minimal.


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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Antonio Restivo
    • 1
  • Roberto Vaglica
    • 1
  1. 1.Dipartimento di Matematica e InformaticaUniversità degli Studi di PalermoPalermoItaly

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