Abstract
Let Σ be a finite alphabet. A set \(\mathcal{R}\) of regular languages over Σ is called rational if there exists a finite set \(\mathcal E\) of regular languages over Σ, such that \(\mathcal{R}\) is a rational subset of the finitely generated semigroup \((\mathcal{S},\cdot)=\langle\mathcal E\rangle\) with \(\mathcal E\) as the set of generators and language concatenation as a product. We prove that for any rational set \(\mathcal{R}\) and any regular language R ⊆ Σ* it is decidable (1) whether \(R\in\mathcal{R}\) or not, and (2) whether \(\mathcal{R}\) is finite or not.
This research was supported in part by the grant No. 10002-251 of the RAS program No. 17 “Parallel computations and multiprocessor systems”
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Afonin, S., Hazova, E. (2005). Membership and Finiteness Problems for Rational Sets of Regular Languages. In: De Felice, C., Restivo, A. (eds) Developments in Language Theory. DLT 2005. Lecture Notes in Computer Science, vol 3572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11505877_8
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DOI: https://doi.org/10.1007/11505877_8
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