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Kleene automata and recursion theory

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Logical Foundations of Computer Science — Tver '92 (LFCS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 620))

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Abstract

Following the introduction of a theoretical computational model on infinite objects, the ω-input Turing machine, we present a new type of infinite automata, the Kleene automata. We show it recognizes exactly the class of arithmetical ω-languages. Essentially, it is a proposisional automaton for which the transition relation is recursive and the interpretation of atomic formulas associated with each state is recursive. The acceptance conditions are built up hierarchically by adding to each level, the recursive disjonctions of negations of the previous level's formulas. The first level is a proposisional temporal logic restricted to the only one temporal operator next. We show the expressive power of this logic to be the class of recursive ω-languages.

Work supported by scholarships from INRS and FCAR.

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References

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Authors and Affiliations

  1. INRS-télécommunications, 3, Place du Commerce, Ile-des-Soeurs, H3E 1H6, Verdun, Québec, Canada

    John Mullins

Authors
  1. John Mullins
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Anil Nerode Mikhail Taitslin

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© 1992 Springer-Verlag Berlin Heidelberg

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Mullins, J. (1992). Kleene automata and recursion theory. In: Nerode, A., Taitslin, M. (eds) Logical Foundations of Computer Science — Tver '92. LFCS 1992. Lecture Notes in Computer Science, vol 620. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023887

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  • DOI: https://doi.org/10.1007/BFb0023887

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55707-4

  • Online ISBN: 978-3-540-47276-6

  • eBook Packages: Springer Book Archive

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