Reversal Hierarchies for Small 2DFAs

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


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.


State Component Positive Instance Full Computation Size Polynomial Generic String 
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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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