The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
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Locality of order-invariant first-order formulas
ACM Transactions on Computational Logic (TOCL)
Foundations of Databases: The Logical Level
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ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
Recognizability Equals Monadic Second-Order Definability for Sets of Graphs of Bounded Tree-Width
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
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LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
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Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
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LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Tree acceptors and some of their applications
Journal of Computer and System Sciences
Regular tree languages definable in FO
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Finding your way in a forest: on different types of trees and their properties
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
First-Order and Monadic Second-Order Model-Checking on Ordered Structures
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Finite model theory on tame classes of structures
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Boundedness of monadic FO over acyclic structures
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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This work deals with the expressive power of logics on finite structures 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 graph-theoretically well-behaved structures. 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.