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Model Checking Vector Addition Systems with one zero-test

Rémi Bonnet ; Alain FInkel ; Jérôme Leroux ; Marc Zeitoun.
We design a variation of the Karp-Miller algorithm to compute, in a forward manner, a finite representation of the cover (i.e., the downward closure of the reachability set) of a vector addition system with one zero-test. This algorithm yields decision procedures for several problems for these&nbsp;[&hellip;]
Published on June 19, 2012
Volume 8, Issue 2

On Separation by Locally Testable and Locally Threshold Testable Languages

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,&nbsp;[&hellip;]
Published on September 18, 2014
Volume 10, Issue 3

Separating Regular Languages with First-Order Logic

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&nbsp;[&hellip;]
Published on March 9, 2016
Volume 12, Issue 1

The Covering Problem

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&nbsp;[&hellip;]
Published on July 20, 2018
Volume 14, Issue 3

Separation for dot-depth two

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&nbsp;[&hellip;]
Published on September 17, 2021
Volume 17, Issue 3
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