State complexity of star and square of union of k regular languages

  • Authors:

  • Yuan Gao;Lila Kari

  • Affiliations:

  • Department of Computer Science, The University of Western Ontario, London, Ontario, Canada;Department of Computer Science, The University of Western Ontario, London, Ontario, Canada

  • Venue:
  • DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
  • Year:
  • 2012

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Abstract

In this paper, we study the state complexities of $(\bigcup\limits_{i=1}^{k} L_i)^*$ and $(\bigcup\limits_{i=1}^{k} L_i)^2$, where Li, 1≤i≤k, k≥2 are regular languages. We obtain exact bounds for both of these multiple combined operations and show that they are much lower than the mathematical compositions of the state complexities of their basic individual component operations, but have similar forms with the state complexities of some participating combined operations.