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Transforming Two-Way Alternating Finite Automata to One-Way Nondeterministic Automata

  • Viliam Geffert
  • Alexander Okhotin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8634)

Abstract

It is proved that a two-way alternating finite automaton (2AFA) with n states can be transformed to an equivalent one-way nondeterministic finite automaton (1NFA) with f(n) = 2Θ(n logn) states, and that this number of states is necessary in the worst case already for the transformation of a two-way automaton with universal nondeterminism (2Π1FA) to a 1NFA. At the same time, an n-state 2AFA is transformed to a 1NFA with (2 n  − 1)2 + 1 states recognizing the complement of the original language, and this number of states is again necessary in the worst case. The difference between these two trade-offs is used to show that complementing a 2AFA requires at least Ω(n logn) states.

Keywords

Transition Function Boolean Function Regular Language Finite Automaton Input String 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2014

Authors and Affiliations

  • Viliam Geffert
    • 1
  • Alexander Okhotin
    • 2
  1. 1.Department of Computer ScienceŠafárik UniversityKošiceSlovakia
  2. 2.Department of Mathematics and StatisticsUniversity of TurkuTurkuFinland

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