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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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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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Tameness and the power of programs over monoids in DA

Nathan Grosshans ; Pierre Mckenzie ; Luc Segoufin.

The program-over-monoid model of computation originates with Barrington's proof that the model captures the complexity class $\mathsf{NC^1}$. Here we make progress in understanding the subtleties of the model. First, we identify a new tameness condition on a class of monoids that entails a natural&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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Enumerating Answers to First-Order Queries over Databases of Low Degree

Arnaud Durand ; Nicole Schweikardt ; Luc Segoufin.

A class of relational databases has low degree if for all $\delta>0$, all but finitely many databases in the class have degree at most $n^{\delta}$, where $n$ is the size of the database. Typical examples are databases of bounded degree or of degree bounded by $\log n$. It is known that over a&nbsp;[&hellip;]

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