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On the State Complexity of Operations on Two-Way Finite Automata

  • Galina Jirásková
  • Alexander Okhotin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5257)

Abstract

The number of states in two-way deterministic finite automata (2DFAs) is considered. It is shown that the state complexity of basic operations is: at least m + n − o(m + n) and at most 4m + n + 1 for union; at least m + n − o(m + n) and at most m + n + 1 for intersection; at least n and at most 4n for complementation; at least \(\Omega(\frac{m}{n}) + \frac{2^{\Omega(n)}}{\log m}\) and at most \(2m^{m+1}\cdot 2^{n^{n+1}}\) for concatenation; at least \(\frac{1}{n} 2^{\frac{n}{2}-1}\) and at most \(2^{O(n^{n+1})}\) for both star and square; between n and n + 2 for reversal; exactly 2n for inverse homomorphism. In each case m and n denote the number of states in 2DFAs for the arguments.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Galina Jirásková
    • 1
  • Alexander Okhotin
    • 2
    • 3
  1. 1.Mathematical InstituteSlovak Academy of SciencesKošiceSlovakia
  2. 2.Academy of Finland 
  3. 3.Department of MathematicsUniversity of TurkuFinland

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