Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
On a monadic NP vs monadic co-NP
Information and Computation
Information and Computation
Counting quantifiers, successor relations, and logarithmic space
Journal of Computer and System Sciences - special issue on complexity theory
Information and Computation - Special issue: logic and computational complexity
Local properties of query languages
Theoretical Computer Science - Special issue on the 6th International Conference on Database Theory—ICDT '97
Logics with counting and local properties
ACM Transactions on Computational Logic (TOCL)
Locality of order-invariant first-order formulas
ACM Transactions on Computational Logic (TOCL)
Logics with aggregate operators
Journal of the ACM (JACM)
Unary Quantifiers, Transitive Closure, and Relations of Large Degree
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Local Normal Forms for First-Order Logic with Applications to Games and Automata
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Expressive Power of Unary Counters
ICDT '97 Proceedings of the 6th International Conference on Database Theory
On the Theory of One-Step Rewriting in Trace Monoids
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Locality of Queries and Transformations
Electronic Notes in Theoretical Computer Science (ENTCS)
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Well-known theorems of Hanf and Gaifman establishing locality of first-order definable properties have been used in many applications. These theorems were recently generalized to other logics, which led to new applications in descriptive complexity and database theory. However, a logical characterization of local properties that correspond to Hanf's and Gaifman's theorems is still lacking. Such a characterization only exists for structures of bounded valence. In this paper, we give logical characterizations of local properties behind Hanf's and Gaifman's theorems. We first deal with an infinitary logic with counting terms and quantifiers that is known to capture Hanf-locality on structures of bounded valence. We show that testing isomorphism of neighborhoods can be added to it without violating Hanf-locality, while increasing its expressive power. We then show that adding local second-order quantification to it caputures precisely all Hanf-local properties. To capture Gaifman-locality, one must also add a (potentially infinite) case statement. We further show that the hierarchy based on the number of variants in the case statement is strict.