Undecidability of the state complexity of composed regular operations

  • Authors:

  • Arto Salomaa;Kai Salomaa;Sheng Yu

  • Affiliations:

  • Turku Centre for Computer Science, Turku, Finland;School of Computing, Queen's University, Kingston, Ontario, Canada;Department of Computer Science, The University of Western Ontario, London, Ontario, Canada

  • Venue:
  • LATA'11 Proceedings of the 5th international conference on Language and automata theory and applications
  • Year:
  • 2011

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Abstract

We consider the regularity-preserving operations of intersection and marked catenation and construct an infinite sequence Ci, i = 1, 2, . . ., of compositions formed from the two operations. We construct also an infinite sequence of polynomials Si, i = 1, 2, . . ., with positive integer coefficients. As a main result we prove that it is undecidable whether or not Si is a state complexity function of Ci. All languages needed are over a fixed alphabet with at most 50 letters. We also consider some implications and generalizations, as well as present some open problems.