Unary language operations and their nondeterministic state complexity

  • Authors:

  • Markus Holzer;Martin Kutrib

  • Affiliations:

  • Institut für Informatik, Technische Universität München, München, Germany;Institut für Informatik, Universität Giessen, Giessen, Germany

  • Venue:
  • DLT'02 Proceedings of the 6th international conference on Developments in language theory
  • Year:
  • 2002

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Abstract

We investigate the costs, in terms of states, of operations on infinite and finite unary regular languages where the languages are represented by nondeterministic finite automata. In particular, we consider Boolean operations, concatenation, iteration, and λ-free iteration. Most of the bounds are tight in the exact number of states, i.e. the number is sufficient and necessary in the worst case. For the complementation of infinite languages a tight bound in the order of magnitude is shown.