Reversal hierarchies for small 2DFAs

Abstract

A two-way deterministic finite automaton with r(n) reversals performs ≤ (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. © 2012 Springer-Verlag.