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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;]

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A decidable characterization of locally testable tree languages

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&nbsp;[&hellip;]

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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;]

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Deciding definability in FO2(<h,<v) on trees

Thomas Place ; Luc Segoufin.

We provide a decidable characterization of regular forest languages definable in FO2(<h,<v). By FO2(<h,<v) we refer to the two variable fragment of first order logic built from the descendant relation and the following sibling relation. In terms of expressive power it corresponds to a fragment of&nbsp;[&hellip;]

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Covering and separation for logical fragments with modular predicates

Thomas Place ; Varun Ramanathan ; Pascal Weil.

For every class $\mathscr{C}$ of word languages, one may associate a decision problem called $\mathscr{C}$-separation. Given two regular languages, it asks whether there exists a third language in $\mathscr{C}$ containing the first language, while being disjoint from the second one. Usually, finding&nbsp;[&hellip;]

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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;]

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Separating regular languages with two quantifier alternations

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,&nbsp;[&hellip;]

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Regular tree languages in low levels of the Wadge Hierarchy

Mikołaj Bojańczyk ; Filippo Cavallari ; Thomas Place ; Michał Skrzypczak.

In this article we provide effective characterisations of regular languages of infinite trees that belong to the low levels of the Wadge hierarchy. More precisely we prove decidability for each of the finite levels of the hierarchy; for the class of the Boolean combinations of open sets&nbsp;[&hellip;]

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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;]

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