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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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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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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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