Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
Information and Computation
A Game-Theoretic Approach to Constraint Satisfaction
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Constraint Satisfaction, Bounded Treewidth, and Finite-Variable Logics
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
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)
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
A Simple Algorithm for Mal'tsev Constraints
SIAM Journal on Computing
A Characterisation of First-Order Constraint Satisfaction Problems
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
On the Descriptive Complexity of Linear Algebra
WoLLIC '08 Proceedings of the 15th international workshop on Logic, Language, Information and Computation
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Recent Results on the Algebraic Approach to the CSP
Complexity of Constraints
Dualities for Constraint Satisfaction Problems
Complexity of Constraints
Universal algebra and hardness results for constraint satisfaction problems
Theoretical Computer Science
On the CSP dichotomy conjecture
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Sherali-Adams relaxations and indistinguishability in counting logics
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
The power of counting logics on restricted classes of finite structures
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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We study the definability of constraint satisfaction problems (CSP) in various fixed-point and infinitary logics. We show that testing the solvability of systems of equations over a finite Abelian group, a tractable CSP that was previously known not to be definable in Datalog, is not definable in an infinitary logic with counting and hence that it is not definable in least fixed point logic or its extension with counting. We relate definability of CSPs to their classification obtained from tame congruence theory of the varieties generated by the algebra of polymorphisms of the template structure. In particular, we show that if this variety admits either the unary or affine type, the corresponding CSP is not definable in the infinitary logic with counting. We also study the complexity of determining whether a CSP omits unary and affine types