Relational queries computable in polynomial time
Information and Control
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Fixpoint extensions of first-order logic and datalog-like languages
Proceedings of the Fourth Annual Symposium on Logic in computer science
Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
Journal of Computer and System Sciences
On a monadic NP vs monadic co-NP
Information and Computation
regular Languages Defined with Generalized Quantifiers
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Counter-Free Automata (M.I.T. research monograph no. 65)
Counter-Free Automata (M.I.T. research monograph no. 65)
Counting and Locality over Finite Structures: A Survey
ESSLLI '97 Revised Lectures from the 9th European Summer School on Logic, Language, and Information: Generalized Quantifiers and Computation
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We give a combinatorial method for proving elementary equivalence in first-order logic FO with counting modulo n quantifiers D_n. Inexpressibility results for FO(D_n) with built-in linear order are also considered. We show that certain divisibility properties of word models are not definable in FO(D_n). We also show that the height of complete n-ary trees cannot be expressed in FO(D_n) with linear order. Interpreting the predicate y=nx as a complete n-ary tree, we show that the predicate y=(n+1)x cannot be defined in FO(D_n) with linear order. This proves the conjecture of Niwinski and Stolboushkin. We also discuss connection between our results and the well-known open problem in circuit complexity theory, whether ACC=NC^1.