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On Shuffle Ideals

Published online by Cambridge University Press:  15 February 2003

Pierre-Cyrille Héam
Pierre-Cyrille Héam*
Affiliation:
Laboratoire d'Informatique de Franche-Comté, Université de Franche-Comté, 16 route de Gray, 25030 Besancon Cedex, France; heampc@lifc.univ-fcomte.fr.
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Abstract


A shuffle ideal is a language which is a finite union of languages of the form A*a1A*...A*ak where A is a finite alphabet and the a i 's are letters. We show how to represent shuffle ideals by special automata and how to compute these representations. We also give a temporal logic characterization of shuffle ideals and we study its expressive power over infinite words. We characterize the complexity of deciding whether a language is a shuffle ideal and we give a new quadratic algorithm for this problem. Finally we also present a characterization by subwords of the minimal automaton of a shuffle ideal and study the complexity of basic operations on shuffle ideals.

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Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 36 , Issue 4 , October 2002, pp. 359 - 384
Copyright
© EDP Sciences, 2002

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