Abstract
We show that Monadic Second Order Logic on ω-words extended with the unbounding quantifier (MSO+U) can define non-Borel sets. We conclude that there is no model of nondeterministic automata with a Borel acceptance condition which captures all of MSO+U. We also give an exact topological complexity of the classes of languages recognized by nondeterministic ωB-, ωS- and ωBS-automata studied by Bojańczyk and Colcombet in [BC06]. Furthermore, we show that corresponding alternating automata have higher topological complexity than nondeterministic ones - they inhabit all finite levels of the Borel hierarchy. © 2010 Springer-Verlag.
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CITATION STYLE
Hummel, S., Skrzypczak, M., & Toruńczyk, S. (2010). On the topological complexity of MSO+U and related automata models. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6281 LNCS, pp. 429–440). https://doi.org/10.1007/978-3-642-15155-2_38
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