Tight lower bound for the state complexity of shuffle of regular languages

  • Authors:

  • Cezar Câmpeanu;Kai Salomaa;Sheng Yu

  • Affiliations:

  • Computing and Information Science Department, Queen's University Kingston, Ontario K7L 3N6, Canada;Computing and Information Science Department, Queen's University Kingston, Ontario K7L 3N6, Canada;Computer Science Department, University of Western Ontario London, Ontario N6A 5B7, Canada

  • Venue:
  • Journal of Automata, Languages and Combinatorics
  • Year:
  • 2002

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Abstract

The upper bound for the state complexity of the shuffle of two regular languages is 2mn -1. We prove that this bound can be reached for some (not necessarily complete) deterministic finite automata with, respectively, m and n states. Our construction uses an alphabet of size 5.