Fixpoint logics, relational machines, and computational complexity
Journal of the ACM (JACM)
Relational Databases and Homogeneity in Logics with Counting
FoIKS '02 Proceedings of the Second International Symposium on Foundations of Information and Knowledge Systems
Relational databases and homogeneity in logics with counting
Acta Cybernetica
On Complexity of Ehrenfeucht-Fraïssé Games
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
First-Order Types and Redundant Relations in Relational Databases
ER '09 Proceedings of the ER 2009 Workshops (CoMoL, ETheCoM, FP-UML, MOST-ONISW, QoIS, RIGiM, SeCoGIS) on Advances in Conceptual Modeling - Challenging Perspectives
Spectra of symmetric powers of graphs and the Weisfeiler-Lehman refinements
Journal of Combinatorial Theory Series B
Lower Bounds for Existential Pebble Games and k-Consistency Tests
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
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How difficult is it to decide whether two finite structures can be distinguished in a given logic? For first order logic, this question is equivalent to the graph isomorphism problem with its well-known complexity theoretic difficulties. Somewhat surprisingly, the situation is much clearer when considering the fragments L/sup k/ of first-order logic whose formulae contain at most k (free or bound) variables (for some k/spl ges/1). We show that for each k/spl ges/2, equivalence in the k-variable logic L/sup k/ is complete for polynomial time under quantifier-free reductions (a weak form of NC/sub 0/ reductions). Moreover, we show that the same completeness result holds for the powerful extension C/sup k/ of L/sup k/ with counting quantifiers (for every k/spl ges/2).