The separation problem for regular languages by piecewise testable languages
Formal Languages and Automata Theory
2013-03-12 v1
Abstract
Separation is a classical problem in mathematics and computer science. It asks whether, given two sets belonging to some class, it is possible to separate them by another set of a smaller class. We present and discuss the separation problem for regular languages. We then give a direct polynomial time algorithm to check whether two given regular languages are separable by a piecewise testable language, that is, whether a sentence can witness that the languages are indeed disjoint. The proof is a reformulation and a refinement of an algebraic argument already given by Almeida and the second author.
Cite
@article{arxiv.1303.2143,
title = {The separation problem for regular languages by piecewise testable languages},
author = {Lorijn van Rooijen and Marc Zeitoun},
journal= {arXiv preprint arXiv:1303.2143},
year = {2013}
}