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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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