Abstract
We introduce partially ordered two-way Büchi automata and characterize their expressive power in terms of fragments of first-order logic FO[<]. Partially ordered two-way Büchi automata are Büchi automata which can change the direction in which the input is processed with the constraint that whenever a state is left, it is never re-entered again. Nondeterministic partially ordered two-way Büchi automata coincide with the first-order fragment Σ2. Our main contribution is that deterministic partially ordered two-way Büchi automata are expressively complete for the first-order fragment Δ2. As an intermediate step, we show that deterministic partially ordered two-way Büchi automata are effectively closed under Boolean operations. A small model property yields coNP-completeness of the emptiness problem and the inclusion problem for deterministic partially ordered two-way Büchi automata.
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