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Published in:
2010 | OriginalPaper | Chapter
Automata with Extremal Minimality Conditions
Authors : Antonio Restivo, Roberto Vaglica
Published in: Developments in Language Theory
Publisher: Springer Berlin Heidelberg
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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.