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Minimal NFA and biRFSA Languages

Published online by Cambridge University Press:  23 May 2008

Michel Latteux ,
Yves Roos  and
Alain Terlutte
Michel Latteux
Affiliation:
Laboratoire d'Informatique Fondamentale de Lille, UMR CNRS 8022, Université de Lille 1, 59655 Villeneuve d'Ascq Cedex, France; michel.latteuxyves.roos@lifl.fr
Yves Roos
Affiliation:
Laboratoire d'Informatique Fondamentale de Lille, UMR CNRS 8022, Université de Lille 1, 59655 Villeneuve d'Ascq Cedex, France; michel.latteuxyves.roos@lifl.fr
Alain Terlutte
Affiliation:
Équipe Grappa–EA 3588, Université de Lille 3, Domaine universitaire du “Pont de bois”, BP 149, 59653 Villeneuve d'Ascq Cedex, France; alain.terlutte@univ-lille3.fr
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Abstract

In this paper, we define the notion of biRFSA which is a residual finate stateautomaton (RFSA) whose the reverse is also an RFSA. The languages recognized bysuch automata are called biRFSA languages. We prove that the canonical RFSA of abiRFSA language is a minimal NFA for this language and that each minimalNFA for this language is a sub-automaton of the canonical RFSA. This leadsto a characterization of the family of biRFSA languages.In the second part of this paper, we define the family of biseparable automata. We prove that every biseparable NFA is uniquely minimal among all NFAs recognizinga same language, improving the result of H. Tamm and E. Ukkonen for bideterministic automata.

Keywords

Residual finite state automata; minimal NFA
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 43 , Issue 2 , April 2009 , pp. 221 - 237
Copyright
© EDP Sciences, 2008

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