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Annual Symposium on Theoretical Aspects of Computer Science

STACS 1998: STACS 98 pp 555–565Cite as

Series-parallel posets: Algebra, automata and languages

  • Automata and Formal Languages III
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1373))

Abstract

In order to model concurrency, we extend automata theory from the usual word languages (sets of labelled linear orders) to sets of labelled series-parallel posets - or, equivalently, to sets of terms in an algebra with two product operations: sequential and parallel. We first consider languages of posets having bounded width, and characterize them using depth-nilpotent algebras. Next we introduce series-rational expressions, a natural generalization of the usual rational expressions, as well as a notion of branching automaton. We show both a Myhill-Nerode theorem and a Kleene theorem. We also look at generalizations.

Part of this work was done while the second author was visiting the Institute of Mathematical Sciences, in Chennai.

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Author information

Authors and Affiliations

  1. CIT Campus, Institute of Mathematical Sciences, 600 113, Chennai, India

    K. Lodaya

  2. LIAFA, Univ. Paris-7 & CNRS, 2 place Jussieu, 75251, Paris Cedex 05, France

    P. Weil

Authors
  1. K. Lodaya
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  2. P. Weil
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Editor information

Michel Morvan Christoph Meinel Daniel Krob

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© 1998 Springer-Verlag

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Lodaya, K., Weil, P. (1998). Series-parallel posets: Algebra, automata and languages. In: Morvan, M., Meinel, C., Krob, D. (eds) STACS 98. STACS 1998. Lecture Notes in Computer Science, vol 1373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028590

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  • DOI: https://doi.org/10.1007/BFb0028590

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64230-5

  • Online ISBN: 978-3-540-69705-3

  • eBook Packages: Springer Book Archive

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