Quotient complexity of ideal languages

  • Authors:

  • Janusz Brzozowski;Galina Jirásková;Baiyu Li

  • Affiliations:

  • David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada;Mathematical Institute, Slovak Academy of Sciences, Košice, Slovakia;David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada

  • Venue:
  • LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
  • Year:
  • 2010

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Abstract

We study the state complexity of regular operations in the class of ideal languages. A language L⊆Σ* is a right (left) ideal if it satisfies L=LΣ* (L=Σ*L). It is a two-sided ideal if L=Σ*LΣ*, and an all-sided ideal if L=Σ* L, the shuffle of Σ* with L. We prefer “quotient complexity” to “state complexity”, and we use quotient formulas to calculate upper bounds on quotient complexity whenever it is convenient. We find tight upper bounds on the quotient complexity of each type of ideal language in terms of the complexity of an arbitrary generator and of its minimal generator, the complexity of the minimal generator, and also on the operations union, intersection, set difference, symmetric difference, concatenation, star and reversal of ideal languages.