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Computing the Rabin Index of a Parity Automaton

Published online by Cambridge University Press:  15 August 2002

Olivier Carton  and
Ramón Maceiras
Olivier Carton
Affiliation:
Institut Gaspard Monge, Université de Marne-la-Vallée, 5 boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2, France; Olivier.Carton@univ-mlv.fr.
Ramón Maceiras
Affiliation:
Institut Gaspard Monge, Université de Marne-la-Vallée, 5 boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2, France; Olivier.Carton@univ-mlv.fr.
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Abstract

The Rabin index of a rational language of infinite words given by a parity automaton with n states is computable in time O(n2c) where c is the cardinality of the alphabet. The number of values used by a parity acceptance condition is always greater than the Rabin index and conversely, the acceptance condition of a parity automaton can always be replaced by an equivalent acceptance condition whose number of used values is exactly the Rabin index. This new acceptance condition can also be computed in time O(n2c).

Keywords

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 33 , Issue 6 , November 1999 , pp. 495 - 505
Copyright
© EDP Sciences, 1999

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