Relational queries computable in polynomial time
Information and Control
A restricted second order logic for finite structures
Information and Computation
An extension of fixpoint logic with a symmetry-based choice construct
Information and Computation
Universality of data retrieval languages
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Definability and Descriptive Complexity on Databases of Bounded Tree-Width
ICDT '99 Proceedings of the 7th International Conference on Database Theory
Fixed-Point Logics on Planar Graphs
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
The Power of Counting Logics on Restricted Classes of Finite Structures
CSL '07/EACSL '07, Proceedings of the 21st international workshop and the 16th Annual Conference of the EACSL on Computer Science Logic
Affine systems of equations and counting infinitary logic
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Fields of logic and computation
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The central open question in the field of descriptive complexity theory is whether or not there is a logic that expresses exactly the polynomial-time computable properties of finite structures. It is known, from the work of Cai, Fürer and Immerman that fixed-point logic with counting (${\ensuremath{\textsf{FP}+\textsf{C}}}$) does not suffice for this purpose. Recent work has shown that natural problems involving systems of linear equations are not definable in this logic. This focuses attention on problems of linear algebra as a possible source of new extensions of the logic. Here, I explore the boundary of definability in ${\ensuremath{\textsf{FP}+\textsf{C}}}$ with respect to problems from linear algebra and look at suggestions on how the logic might be extended.