Testing membership in commutative transformation semigroups

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


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 (NC3 in parallel) with threshold zero or one, and NP-complete otherwise.


Permutation Group Commutative Semigroup Parallel Complexity Membership Problem Transformation Semigroup 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Martin Beaudry
    • 1
  1. 1.School of Computer ScienceMcGill UniversityMontréalCanada

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