Abstract
It is proved that if definability of regular languages in the \(\Sigma _n\) fragment of the first-order logic on finite words is decidable, then it is decidable also for the \(\Delta _{n+1}\) fragment. In particular, the decidability for \(\Delta _5\) 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.
The first author was partially supported by CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds through the programs FEDER, under the partnership agreement PT2020. The last two authors were supported by grant 15-02862S of the Czech Science Foundation.
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Almeida, J., Bartoňová, J., Klíma, O., Kunc, M. (2015). On Decidability of Intermediate Levels of Concatenation Hierarchies. In: Potapov, I. (eds) Developments in Language Theory. DLT 2015. Lecture Notes in Computer Science(), vol 9168. Springer, Cham. https://doi.org/10.1007/978-3-319-21500-6_4
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DOI: https://doi.org/10.1007/978-3-319-21500-6_4
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