4 research outputs found
Partially ordered two-way Büchi automata
We introduce partially ordered two-way Büchi automata over infinite words. As for finite words, the nondeterministic variant recognizes the fragment Sigma2 of first-order logic FO[<] and the deterministic version yields the Delta2-definable omega-languages. As a byproduct of our results, we show that deterministic partially ordered two-way Büchi automata are effectively closed under Boolean operations.
In addition, we have coNP-completeness results for the emptiness problem and the inclusion problem over deterministic partially ordered two-way Büchi automata
Partially Ordered Two-way B\"uchi Automata
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.Comment: The results of this paper were presented at CIAA 2010; University of
Stuttgart, Computer Scienc