Combining regular expressions with (near-)optimal brzozowski automata

  • Authors:

  • Michiel Frishert;Bruce W. Watson

  • Affiliations:

  • Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, Eindhoven, The Netherlands;Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, Eindhoven, The Netherlands

  • Venue:
  • CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
  • Year:
  • 2004

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Abstract

Derivatives of regular expressions were first introduced by Brzozowski in [1]. By recursively computing all derivatives of a regular expression, and associating a state with each unique derivative, a deterministic finite automaton can be constructed. Convergence of this process is guaranteed if uniqueness of regular expressions is recognized modulo associativity, commutativity, and idempotence of the union operator. Additionaly, through simplification based on the identities for regular expressions, the number of derivatives can be further reduced.