Abstract
Given a class
of languages, let Pol(
) be the polynomial closure of
, that is, the smallest class of languages containing
and closed under the operations union and marked product L a L', where a is a letter. We determine the polynomial closure of various classes of rational languages and we study the properties of polynomial closures. For instance, if
is closed under quotients (resp. quotients and inverse morphism) then Pol(
) has the same property. Our main result shows that if
is a boolean algebra closed under quotients then Pol(
) is closed under intersection. As an application, we refine the concatenation hierarchy introduced by Straubing and we show that the levels 1/2 and 3/2 of this hierarchy are decidable.
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© 1987 Springer-Verlag Berlin Heidelberg
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Arfi, M. (1987). Polynomial operations on rational languages. In: Brandenburg, F.J., Vidal-Naquet, G., Wirsing, M. (eds) STACS 87. STACS 1987. Lecture Notes in Computer Science, vol 247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0039607
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DOI: https://doi.org/10.1007/BFb0039607
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