Logics with counting and local properties
ACM Transactions on Computational Logic (TOCL)
A uniform method for proving lower bounds on the computational complexity of logical theories
Handbook of logic in computer science
Deciding first-order properties of locally tree-decomposable structures
Journal of the ACM (JACM)
On the Forms of Locality over Finite Models
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Word problems requiring exponential time(Preliminary Report)
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Existential Positive Types and Preservation under Homomorphisisms
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Fixed-Parameter Hierarchies inside PSPACE
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Approximation Schemes for First-Order Definable Optimisation Problems
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Preservation under extensions on well-behaved finite structures
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
The Compositional Method and Regular Reachability
Electronic Notes in Theoretical Computer Science (ENTCS)
Database theory: query languages
Algorithms and theory of computation handbook
Compositional failure detection in structured transition systems
CIAA'11 Proceedings of the 16th international conference on Implementation and application of automata
The Complexity of Decomposing Modal and First-Order Theories
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
LTL-Model-Checking via model composition
RP'12 Proceedings of the 6th international conference on Reachability Problems
An Optimal Gaifman Normal Form Construction for Structures of Bounded Degree
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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Gaifman's locality theorem states that every first-order sentence is equivalent to a local sentence. We show that there is no elementary bound on the length of the local sentence in terms of the original. The classical Łoś-Tarski theorem states that every first-order sentence preserved under extensions is equivalent to an existential sentence. We show that there is no elementary bound on the length of the existential sentence in terms of the original. Recently, variants of the Łoś-Tarski theorem have been proved for certain classes of finite structures, among them the class of finite acyclic structures and more generally classes of structures of bounded tree width. Our lower bound also applies to these variants. We further prove that a version of the Feferman-Vaught theorem based on a restriction by formula length necessarily entails a non-elementary blow-up in formula size. All these results are based on a similar technique of encoding large numbers by trees of small height in such a way that small formulas can speak about these numbers. Notably, our lower bounds do not apply to restrictions of the results to structures of bounded degree. For such structures, we obtain elementary upper bounds in all cases. However, even there we can prove at least doubly exponential lower bounds.