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Reversal Hierarchies for Small 2DFAs

  • Christos A. Kapoutsis
  • Giovanni Pighizzini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7464)

Abstract

A two-way deterministic finite automaton with r(n) reversals performs ≤ r (n) input head reversals on every n-long input. Let 2D[r(n)] be all families of problems solvable by such automata of size polynomial in the index of the family. Then the reversal hierarchy 2D[0] ⊆ 2D[1] ⊆ 2D[2] ⊆ ⋯ is strict, but 2D[O(1)] = 2D[o(n)]. Moreover, the inner-reversal hierarchy 2D(0) ⊆ 2D(1) ⊆ 2D(2) ⊆ ⋯ , where now the bound is only for reversals strictly between the input end-markers, is also strict.

Keywords

State Component Positive Instance Full Computation Size Polynomial Generic 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 Berlin Heidelberg 2012

Authors and Affiliations

  • Christos A. Kapoutsis
    • 1
  • Giovanni Pighizzini
    • 2
  1. 1.LIAFAUniversité Paris VIIFrance
  2. 2.DIUniversità degli Studi di MilanoItalia

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