When won't membership queries help?
Selected papers of the 23rd annual ACM symposium on Theory of computing
On the algebraic structure of combinatorial problems
Theoretical Computer Science
Foundations of Inductive Logic Programming
Foundations of Inductive Logic Programming
Tractable conservative Constraint Satisfaction Problems
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Learnability of quantified formulas
Theoretical Computer Science
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
The expressive rate of constraints
Annals of Mathematics and Artificial Intelligence
A dichotomy theorem for constraint satisfaction problems on a 3-element set
Journal of the ACM (JACM)
A Simple Algorithm for Mal'tsev Constraints
SIAM Journal on Computing
Tractability and learnability arising from algebras with few subpowers
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
Learning intersection-closed classes with signatures
Theoretical Computer Science
Quantified Constraint Satisfaction and the Polynomially Generated Powers Property
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Constraints, consistency and closure
Artificial Intelligence
Constraint Satisfaction Problems of Bounded Width
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Survey: Colouring, constraint satisfaction, and complexity
Computer Science Review
On the CSP dichotomy conjecture
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Meditations on quantified constraint satisfaction
Logic and Program Semantics
An Algebraic Preservation Theorem for Aleph-Zero Categorical Quantified Constraint Satisfaction
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Generic expression hardness results for primitive positive formula comparison
Information and Computation
Journal of Artificial Intelligence Research
The complexity of conservative valued CSPs
Journal of the ACM (JACM)
The complexity of finite-valued CSPs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
The complexity of the counting constraint satisfaction problem
Journal of the ACM (JACM)
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A constraint language $\Gamma$ on a finite set $A$ has been called polynomially expressive if the number of $n$-ary relations expressible by $\exists\wedge$-atomic formulas over $\Gamma$ is bounded by $\exp(O(n^k))$ for some constant $k$. It has recently been discovered that this property is characterized by the existence of a $(k+1)$-ary polymorphism satisfying certain identities; such polymorphisms are called $k$-edge operations and include Mal'cev and near-unanimity operations as special cases. We prove that if $\Gamma$ is any constraint language which, for some $k1$, has a $k$-edge operation as a polymorphism, then the constraint satisfaction problem for $\langle\Gamma\rangle$ (the closure of $\Gamma$ under $\exists\wedge$-atomic expressibility) is globally tractable. We also show that the set of relations definable over $\Gamma$ using quantified generalized formulas is polynomially exactly learnable using improper equivalence queries.