Partially Ordered Two-way B\"uchi Automata
Abstract
We introduce partially ordered two-way B\"uchi automata and characterize their expressive power in terms of fragments of first-order logic FO[<]. Partially ordered two-way B\"uchi automata are B\"uchi 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 B\"uchi automata coincide with the first-order fragment Sigma2. Our main contribution is that deterministic partially ordered two-way B\"uchi automata are expressively complete for the first-order fragment Delta2. As an intermediate step, we show that deterministic partially ordered two-way B\"uchi 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 B\"uchi automata.
Keywords
Cite
@article{arxiv.1006.2719,
title = {Partially Ordered Two-way B\"uchi Automata},
author = {Manfred Kufleitner and Alexander Lauser},
journal= {arXiv preprint arXiv:1006.2719},
year = {2015}
}
Comments
The results of this paper were presented at CIAA 2010; University of Stuttgart, Computer Science