Language operations with regular expressions of polynomial size

  • Authors:

  • Hermann Gruber;Markus Holzer

  • Affiliations:

  • Institut für Informatik, Justus-Liebig-Universität Giessen, Arndtstraβe 2, D-35392 Giessen, Germany;Institut für Informatik, Justus-Liebig-Universität Giessen, Arndtstraβe 2, D-35392 Giessen, Germany

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2009

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Abstract

This work deals with questions regarding to what extent regularity-preserving language operations affect the descriptional complexity of regular expressions. Some language operations are identified which are feasible for regular expressions in the sense that the result of the operation can be represented as a regular expression of size polynomial in that of the operands. We prove that taking language quotients, in particular the prefix and suffix closures, of a regular set can incur at most a quadratic blow-up on the required expression size. The circular shift operation can cause only a cubic increase in size and at least a quadratic bloat can be necessary in the worst case.