Efficient Separability of Regular Languages by Subsequences and Suffixes

TL;DR

This paper explores the conditions under which two regular languages can be separated by simple subclasses like piecewise- and suffix-testable languages, providing characterizations and polynomial-time decision procedures.

Contribution

It offers new characterizations for separability of regular languages by simple subclasses and analyzes the computational complexity of deciding such separability.

Findings

Characterizations of separability conditions

Polynomial-time algorithms for decision problems

Applicability to nondeterministic automata

Abstract

When can two regular word languages K and L be separated by a simple language? We investigate this question and consider separation by piecewise- and suffix-testable languages and variants thereof. We give characterizations of when two languages can be separated and present an overview of when these problems can be decided in polynomial time if K and L are given by nondeterministic automata.