A generic characterization of Pol(C)
Formal Languages and Automata Theory
2018-02-20 v1
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).
Cite
@article{arxiv.1802.06141,
title = {A generic characterization of Pol(C)},
author = {Thomas Place and Marc Zeitoun},
journal= {arXiv preprint arXiv:1802.06141},
year = {2018}
}