State Complexity of Basic Operations on Finite Languages

  • C. Câmpeanu
  • K. CulikII
  • Kai Salomaa
  • Sheng Yu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2214)


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 mstate and an n-state DFA, respectively, with m > n is accepted by a DFA of (mn + 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 · 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.


State Complexity Basic Operation Starting State Regular Language Sink State 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • C. Câmpeanu
    • 1
  • K. CulikII
    • 2
  • Kai Salomaa
    • 3
  • Sheng Yu
    • 3
  1. 1.Fundamentals of Computer Science DepartmentFaculty of Mathematics University of BucharestRomania
  2. 2.Department of Computer ScienceUniversity of South CarolinaColumbiaUSA
  3. 3.Department of Computer ScienceThe University of Western OntarioLondonCanada

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