Operations on Unambiguous Finite Automata

  • Jozef JirásekJr.
  • Galina Jirásková
  • Juraj Šebej
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9840)


A nondeterministic finite automaton is unambiguous if it has at most one accepting computation on every input string. We investigate the complexity of basic regular operations on languages represented by unambiguous finite automata. We get tight upper bounds for intersection (mn), left and right quotients (\(2^n-1\)), positive closure (\({3\over 4}\cdot 2^n-1\)), star (\({3\over 4}\cdot 2^n\)), shuffle (\(2^{mn}-1\)), and concatenation (\({3\over 4}\cdot 2^{m+n}-1\)). To prove tightness, we use a binary alphabet for intersection and left and right quotients, a ternary alphabet for star and positive closure, a five-letter alphabet for shuffle, and a seven-letter alphabet for concatenation. We also get some partial results for union and complementation.


State Complexity Regular Language Finite Automaton Input String Tree Automaton 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Jozef JirásekJr.
    • 1
    • 2
  • Galina Jirásková
    • 1
  • Juraj Šebej
    • 2
  1. 1.Mathematical InstituteSlovak Academy of SciencesKošiceSlovakia
  2. 2.Faculty of Science, Institute of Computer ScienceP.J. Šafárik UniversityKošiceSlovakia

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