5 results
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 […]
Published on October 20, 2010
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 […]
Published on September 24, 2013
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 […]
Published on September 29, 2012
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 […]
Published on May 10, 2022
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 […]
Published on August 2, 2022