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March 2009 Towards a characterization of order-invariant queries over tame graphs
Michael A. Benedikt, Luc Segoufin
J. Symbolic Logic 74(1): 168-186 (March 2009). DOI: 10.2178/jsl/1231082307

Abstract

This work deals with the expressive power of logics on finite graphs with access to an additional “arbitrary” linear order. The queries that can be expressed this way are the order-invariant queries for the logic. For the standard logics used in computer science, such as first-order logic, it is known that access to an arbitrary linear order increases the expressiveness of the logic. However, when we look at the separating examples, we find that they have satisfying models whose Gaifman Graph is complex — unbounded in valence and in treewidth. We thus explore the expressiveness of order-invariant queries over well-behaved graphs. We prove that first-order order-invariant queries over strings and trees have no additional expressiveness over first-order logic in the original signature. We also prove new upper bounds on order-invariant queries over bounded treewidth and bounded valence graphs. Our results make use of a new technique of independent interest: the application of algebraic characterizations of definability to show collapse results.

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Michael A. Benedikt. Luc Segoufin. "Towards a characterization of order-invariant queries over tame graphs." J. Symbolic Logic 74 (1) 168 - 186, March 2009. https://doi.org/10.2178/jsl/1231082307

Information

Published: March 2009
First available in Project Euclid: 4 January 2009

zbMATH: 1161.03018
MathSciNet: MR2499425
Digital Object Identifier: 10.2178/jsl/1231082307

Rights: Copyright © 2009 Association for Symbolic Logic

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Vol.74 • No. 1 • March 2009
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