Complementing Two-Way Finite Automata

  • Viliam Geffert
  • Carlo Mereghetti
  • Giovanni Pighizzini
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3572)


We study the relationship between the sizes of two-way finite automata accepting a language and its complement. In the deterministic case, by adapting Sipser’s method, for a given automaton (2dfa) with n states we build an automaton accepting the complement with at most 4n states, independently of the size of the input alphabet. Actually, we show a stronger result, by presenting an equivalent 4n–state 2dfa that always halts.

For the nondeterministic case, using a variant of inductive counting, we show that the complement of a unary language, accepted by an n–state two-way automaton (2nfa), can be accepted by an O(n8)–state 2nfa. Here we also make the 2nfa halting. This allows the simulation of unary 2nfa’s by probabilistic Las Vegas two-way automata with O(n8) states.


automata and formal languages descriptional complexity 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Viliam Geffert
    • 1
  • Carlo Mereghetti
    • 2
  • Giovanni Pighizzini
    • 3
  1. 1.Department of Computer ScienceP. J. Šafárik UniversityKošiceSlovakia
  2. 2.Dipartimento di Scienze dell’InformazioneUniversità degli Studi di MilanoMilanoItaly
  3. 3.Dipartimento di Informatica e ComunicazioneUniversità degli Studi di MilanoMilanoItaly

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