State Complexity of Basic Operations on Finite Languages

  • Authors:

  • Cezar Campeanu;Karel Culik, II;Kai Salomaa;Sheng Yu

  • Affiliations:

  • -;-;-;-

  • Venue:
  • WIA '99 Revised Papers from the 4th International Workshop on Automata Implementation
  • Year:
  • 1999

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Abstract

The state complexity of basic operations on regular languages has been studied in [9,10,11]. Here we focus on finite languages. We show that the catenation of two finite languages accepted by an m- state and an n-state DFA, respectively, with m n is accepted by a DFA of (m - n + 3)2n-2 - 1 states in the two-letter alphabet case, and this bound is shown to be reachable. We also show that the tight upperbounds for the number of states of a DFA that accepts the star of an n-state finite language is 2n-3 + 2n-4 in the two-letter alphabet case. The same bound for reversal is 3 驴 2p-1 - 1 when n is even and 2p - 1 when n is odd. Results for alphabets of an arbitrary size are also obtained. These upper-bounds for finite languages are strictly lower than the corresponding ones for general regular languages.