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Wreath Products of Forest Algebras, with Applications to Tree Logics

Mikolaj Bojanczyk ; Igor Walukiewicz ; Howard Straubing.

We use the recently developed theory of forest algebras to find algebraic characterizations of the languages of unranked trees and forests definable in various logics. These include the temporal logics CTL and EF, and first-order logic over the ancestor relation. While the characterizations are in&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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An extension of data automata that captures XPath

Mikołaj Bojańczyk ; Sławomir Lasota.

We define a new kind of automata recognizing properties of data words or data trees and prove that the automata capture all queries definable in Regular XPath. We show that the automata-theoretic approach may be applied to answer decidability and expressibility questions for XPath.

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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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Optimizing tree decompositions in MSO

Mikołaj Bojańczyk ; Michał Pilipczuk.

The classic algorithm of Bodlaender and Kloks [J. Algorithms, 1996] solves the following problem in linear fixed-parameter time: given a tree decomposition of a graph of (possibly suboptimal) width k, compute an optimum-width tree decomposition of the graph. In this work, we prove that this problem&nbsp;[&hellip;]

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