An Explicit Formula for the Intersection of Two Polynomials of Regular Languages
نویسنده
چکیده
Let L be a set of regular languages of A∗. An L-polynomial is a finite union of products of the form L0a1L1 · · · anLn, where each ai is a letter of A and each Li is a language of L. We give an explicit formula for computing the intersection of two L-polynomials. Contrary to Arfi’s formula (1991) for the same purpose, our formula does not use complementation and only requires union, intersection and quotients. Our result also implies that if L is closed under union, intersection and quotient, then its polynomial closure, its unambiguous polynomial closure and its left [right] deterministic polynomial closure are closed under the same operations.
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تاریخ انتشار 2013