6 results
Thomas Place ; Marc Zeitoun.
An important endeavor in computer science is to understand the expressive power of logical formalisms over discrete structures, such as words. Naturally, "understanding" is not a mathematical notion. This investigation requires therefore a concrete objective to capture this understanding. In the […]
Published on July 20, 2018
Thomas Place.
We investigate a famous decision problem in automata theory: separation. Given a class of language C, the separation problem for C takes as input two regular languages and asks whether there exists a third one which belongs to C, includes the first one and is disjoint from the second. Typically, […]
Published on November 16, 2018
Thomas Place ; Lorijn van Rooijen ; Marc Zeitoun.
A separator for two languages is a third language containing the first one and disjoint from the second one. We investigate the following decision problem: given two regular input languages, decide whether there exists a locally testable (resp. a locally threshold testable) separator. In both cases, […]
Published on September 18, 2014
Thomas Place ; Luc Segoufin.
A regular tree language L is locally testable if membership of a tree in L depends only on the presence or absence of some fix set of neighborhoods in the tree. In this paper we show that it is decidable whether a regular tree language is locally testable. The decidability is shown for ranked trees […]
Published on November 22, 2011
Thomas Place ; Marc Zeitoun.
Given two languages, a separator is a third language that contains the first one and is disjoint from the second one. We investigate the following decision problem: given two regular input languages of finite words, decide whether there exists a first-order definable separator. We prove that in […]
Published on March 9, 2016
Thomas Place ; Marc Zeitoun.
The dot-depth hierarchy of Brzozowski and Cohen classifies the star-free languages of finite words. By a theorem of McNaughton and Papert, these are also the first-order definable languages. The dot-depth rose to prominence following the work of Thomas, who proved an exact correspondence with the […]
Published on September 17, 2021