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arXiv · 1802.06141

A generic characterization of Pol(C)

Thomas Place·Marc Zeitoun
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Abstract

We investigate the polynomial closure operation (C -> Pol(C)) defined on classes of regular languages. We present an interesting and useful connection relating the separation problem for the class C and the membership problem for it polynomial closure Pol(C). This connection is formulated as an algebraic characterization of Pol(C) which holds when C is an arbitrary \pvari of regular languages and whose statement is parameterized by C-separation. Its main application is an effective reduction from Pol(C)-membership to C-separation. Thus, as soon as one designs a C-separation algorithm, this yields "for free" a membership algorithm for the more complex class Pol(C).

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Thomas Place, Marc Zeitoun. 2018-02-16. A generic characterization of Pol(C). https://arxiv.org/abs/1802.06141

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