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Automata on Linear Orderings

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Mathematical Foundations of Computer Science 2001 (MFCS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2136))

Abstract

We consider words indexed by linear orderings. These extend finite, (bi-)infinite words and words on ordinals. We introduce automata and rational expressions for words on linear orderings. We prove that for countable scattered linear orderings they are equivalent. This result extends Kleene’s theorem. The proofs are effective.

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Author information

Authors and Affiliations

  1. Institut de Mathématique et d’Informatique, Université de Mons-Hainaut, Le Pentagone, 6 avenue du Champ de Mars, B-7000, Mons, Belgium

    Véronique Bruyère

  2. Institut Gaspard Monge, Université de Marne-la-Vallée, 5 boulevard Descartes, F-77454, Marne-la-Vallée Cedex 2, France

    Olivier Carton

Authors
  1. Véronique Bruyère
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  2. Olivier Carton
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Editor information

Editors and Affiliations

  1. Mathematical Institute, AS CR, Žitná 25, 115 67, Praha 1, Czech Republic

    Jiří Sgall

  2. Faculty of Mathematics and Physics Institute for Theoretical Computer Science (ITI), Charles University, Malostranské náměstí 25, 118 00, Praha 1, Czech Republic

    Aleš Pultr  & Petr Kolman  & 

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© 2001 Springer-Verlag Berlin Heidelberg

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Bruyère, V., Carton, O. (2001). Automata on Linear Orderings. In: Sgall, J., Pultr, A., Kolman, P. (eds) Mathematical Foundations of Computer Science 2001. MFCS 2001. Lecture Notes in Computer Science, vol 2136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44683-4_21

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  • DOI: https://doi.org/10.1007/3-540-44683-4_21

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42496-3

  • Online ISBN: 978-3-540-44683-5

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