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Describing Periodicity in Two-Way Deterministic Finite Automata Using Transformation Semigroups

  • Michal Kunc
  • Alexander Okhotin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6795)

Abstract

A framework for the study of periodic behaviour of two-way deterministic finite automata (2DFA) is developed. Computations of 2DFAs are represented by a two-way analogue of transformation semigroups, every element of which describes the behaviour of a 2DFA on a certain string x. A subsemigroup generated by this element represents the behaviour on strings in x  + . The main contribution of this paper is a description of all such monogenic subsemigroups up to isomorphism. This characterization is then used to show that transforming an n-state 2DFA over a one-letter alphabet to an equivalent sweeping 2DFA requires exactly n + 1 states, and transforming it to a one-way automaton requires exactly \(\max_{0 \leqslant \ell \leqslant n} G(n-\ell)+\ell+1\) states, where G(k) is the maximum order of a permutation of k elements.

Keywords

Regular Language Partial Transformation Transformation Semigroup Information Processing Letter Nondeterministic Automaton 
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 Berlin Heidelberg 2011

Authors and Affiliations

  • Michal Kunc
    • 1
  • Alexander Okhotin
    • 2
    • 3
  1. 1.Masaryk UniversityCzech Republic
  2. 2.Department of MathematicsUniversity of TurkuFinland
  3. 3.Academy of FinlandFinland

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