Two-Way Unary Automata versus Logarithmic Space

  • Viliam Geffert
  • Giovanni Pighizzini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6224)


We show that each n-state unary 2nfa (a two-way nondeterministic finite automaton) can be simulated by an equivalent 2ufa (an unambiguous 2nfa) with a polynomial number of states. Moreover, if L = NL (the classical logarithmic space classes), then each unary 2nfa can be converted into an equivalent 2dfa (a deterministic two-way automaton), still keeping polynomial the number of states. This shows a connection between the standard logarithmic space complexity and the state complexity of two-way unary automata: it indicates that L could be separated from NL by proving a superpolynomial gap, in the number of states, for the conversion from unary 2NFAs to 2DFAs.


unary regular languages finite automata state complexity logarithmic space space complexity 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Viliam Geffert
    • 1
  • Giovanni Pighizzini
    • 2
  1. 1.Department of Computer ScienceP. J. Šafárik UniversityKošiceSlovakia
  2. 2.Dipartimento di Informatica e ComunicazioneUniversità degli Studi di MilanoMilanoItaly

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