Verifiable properties of database transactions
PODS '96 Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Dynamic tree isomorphism via first-order updates to a relational database
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
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
On TC/sup 0/, AC/sup 0/, and Arithmetic Circuits
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
Completeness results for graph isomorphism
Journal of Computer and System Sciences
| Hi-index | 0.00 |
We present new expressibility lower bounds for a logic with a weak form of ordering using model theoretic games. Our lower bound is on first-order logic augmented with counting quantifiers, a logical language that over structures with a total-ordering has exactly the power of the class TC/sup 0/. We prove that it cannot express a property ORD in L, over structures with a successor relation. This holds even in light of the fact that the class L itself has a logical characterization as the properties expressible in first-order logic with a deterministic transitive closure operator over structures with a successor relation. The proof uses an extension of the well known Ehrenfeucht-Fraisse Games for logics with counting. We also show that ORD is actually complete for L (via quantifier free projections), and this fact is of independent interest.