Equations Defining the Polynomial Closure of a Lattice of Regular Languages
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چکیده
The polynomial closure Pol(L) of a class of languages L of A is the set of languages that are finite unions of marked products of the form L0a1L1 · · · anLn, where the ai are letters and the Li are elements of L. The main result of this paper gives an equational description of Pol(L), given an equational description of L, when 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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تاریخ انتشار 2009