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FO2(<,+1,~) on data trees, data tree automata and branching vector addition systems

Florent Jacquemard ; Luc Segoufin ; Jerémie Dimino.

A data tree is an unranked ordered tree where each node carries a label from a finite alphabet and a datum from some infinite domain. We consider the two variable first order logic FO2(<,+1,~) over data trees. Here +1 refers to the child and the next sibling relations while < refers to the&nbsp;[&hellip;]

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Bottom-up automata on data trees and vertical XPath

Diego Figueira ; Luc Segoufin.

A data tree is a finite tree whose every node carries a label from a finite alphabet and a datum from some infinite domain. We introduce a new model of automata over unranked data trees with a decidable emptiness problem. It is essentially a bottom-up alternating automaton with one register that can&nbsp;[&hellip;]

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Tree Languages Defined in First-Order Logic with One Quantifier Alternation

Mikolaj Bojanczyk ; Luc Segoufin.

We study tree languages that can be defined in \Delta_2 . These are tree languages definable by a first-order formula whose quantifier prefix is forall exists, and simultaneously by a first-order formula whose quantifier prefix is . For the quantifier free part we consider two signatures, either the&nbsp;[&hellip;]

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Unary negation

Luc Segoufin ; Balder ten Cate.

We study fragments of first-order logic and of least fixed point logic that allow only unary negation: negation of formulas with at most one free variable. These logics generalize many interesting known formalisms, including modal logic and the $\mu$-calculus, as well as conjunctive queries and&nbsp;[&hellip;]

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First-order query evaluation on structures of bounded degree

Wojciech Kazana ; Luc Segoufin.

We consider the enumeration problem of first-order queries over structures of bounded degree. It was shown that this problem is in the Constant-Delaylin class. An enumeration problem belongs to Constant-Delaylin if for an input of size n it can be solved by: - an O(n) precomputation phase building&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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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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Piecewise testable tree languages

Mikołaj Bojańczyk ; Luc Segoufin ; Howard Straubing.

This paper presents a decidable characterization of tree languages that can be defined by a boolean combination of Sigma_1 sentences. This is a tree extension of the Simon theorem, which says that a string language can be defined by a boolean combination of Sigma_1 sentences if and only if its&nbsp;[&hellip;]

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Datalog Rewritings of Regular Path Queries using Views

Nadime Francis ; Luc Segoufin ; Cristina Sirangelo.

We consider query answering using views on graph databases, i.e. databases structured as edge-labeled graphs. We mainly consider views and queries specified by Regular Path Queries (RPQ). These are queries selecting pairs of nodes in a graph database that are connected via a path whose sequence of&nbsp;[&hellip;]

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First-order queries on classes of structures with bounded expansion

Wojtek Kazana ; Luc Segoufin.

We consider the evaluation of first-order queries over classes of databases with bounded expansion. The notion of bounded expansion is fairly broad and generalizes bounded degree, bounded treewidth and exclusion of at least one minor. It was known that over a class of databases with bounded&nbsp;[&hellip;]

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