Abstract
The polynomial closure Pol\((\mathcal{L})\) of a class of languages \(\mathcal{L}\) of A * is the set of languages that are finite unions of marked products of the form L 0 a 1 L 1 ... a n L n , where the a i are letters and the L i are elements of \(\mathcal{L}\).
The main result of this paper gives an equational description of Pol\((\mathcal{L})\), given an equational description of \(\mathcal{L}\), when \(\mathcal{L}\) is a lattice of regular languages closed under quotients, or a quotienting algebra of languages, as we call it in the sequel. The term “equational description” refers to a recent paper [5], where it was shown that any lattice of regular languages can be defined by a set of profinite equations. More formally, our main result can be stated as follows:
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Branco, M.J.J., Pin, JÉ. (2009). Equations Defining the Polynomial Closure of a Lattice of Regular Languages. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds) Automata, Languages and Programming. ICALP 2009. Lecture Notes in Computer Science, vol 5556. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02930-1_10
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