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arXiv · 1006.2719

Partially Ordered Two-way Büchi Automata

Manfred Kufleitner·Alexander Lauser
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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 Sigma2. Our main contribution is that deterministic partially ordered two-way Büchi automata are expressively complete for the first-order fragment Delta2. 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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Manfred Kufleitner, Alexander Lauser. 2011-08-25. Partially Ordered Two-way Büchi Automata. https://doi.org/10.1007/978-3-642-18098-9_20

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