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Testing membership in commutative transformation semigroups

Complexity

Part of the Lecture Notes in Computer Science book series (LNCS,volume 267)

Abstract

Given a finite set X of points, a finite set of commuting transformations over X (generators), and another transformation f over X, we analyze the complexity of the problem of deciding whether f can be obtained by composition of the generators. We show that the complexity varies with the threshold of the semigroup: polynomial-time (NC 3 in parallel) with threshold zero or one, and NP-complete otherwise.

Keywords

  • Permutation Group
  • Commutative Semigroup
  • Parallel Complexity
  • Membership Problem
  • Transformation Semigroup

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© 1987 Springer-Verlag Berlin Heidelberg

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Beaudry, M. (1987). Testing membership in commutative transformation semigroups. In: Ottmann, T. (eds) Automata, Languages and Programming. ICALP 1987. Lecture Notes in Computer Science, vol 267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18088-5_47

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  • DOI: https://doi.org/10.1007/3-540-18088-5_47

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18088-3

  • Online ISBN: 978-3-540-47747-1

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