One alternation can be more powerful than randomization in small and fast two-way finite automata

Authors:
Kaspars Balodis
Affiliations:
Faculty of Computing, University of Latvia, Riga, Latvia
Venue:
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
Year:
2013

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Abstract

We show a family of languages that can be recognized by a family of linear-size alternating one-way finite automata with one alternation but cannot be recognized by any family of polynomial-size bounded-error two-way probabilistic finite automata with the expected runtime bounded by a polynomial. In terms of finite automata complexity theory this means that neither 1Σ2 nor 1Π2 is contained in 2P2.