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.
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© 2012 Springer-Verlag Berlin Heidelberg
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Kapoutsis, C.A., Pighizzini, G. (2012). Reversal Hierarchies for Small 2DFAs. In: Rovan, B., Sassone, V., Widmayer, P. (eds) Mathematical Foundations of Computer Science 2012. MFCS 2012. Lecture Notes in Computer Science, vol 7464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32589-2_49
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DOI: https://doi.org/10.1007/978-3-642-32589-2_49
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