Abstract
It is proved that if definability of regular languages in the Σn fragment of the first-order logic on finite words is decidable, then it is decidable also for the Δn+1 fragment. In particular, the decidability for Δ5 is obtained. More generally, for every concatenation hierarchy of regular languages, it is proved that decidability of one of its half levels implies decidability of the intersection of the following half level with its complement.
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CITATION STYLE
Almeida, J., Bartoňová, J., Klíma, O., & Kunc, M. (2015). On decidability of intermediate levels of concatenation hierarchies. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9168, pp. 58–70). Springer Verlag. https://doi.org/10.1007/978-3-319-21500-6_4
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