Communications of the ACM
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Learning Nested Differences of Intersection-Closed Concept Classes
Machine Learning
Prediction-preserving reducibility
Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
Learning Conjunctions of Horn Clauses
Machine Learning - Computational learning theory
Cryptographic limitations on learning Boolean formulae and finite automata
Journal of the ACM (JACM)
Characterising tractable constraints
Artificial Intelligence
When won't membership queries help?
Selected papers of the 23rd annual ACM symposium on Theory of computing
Tractable constraints on ordered domains
Artificial Intelligence
Exact learning Boolean functions via the monotone theory
Information and Computation
Learning counting functions with queries
Theoretical Computer Science
Closure properties of constraints
Journal of the ACM (JACM)
Theories of computability
An efficient membership-query algorithm for learning DNF with respect to the uniform distribution
Journal of Computer and System Sciences
Constraints, consistency and closure
Artificial Intelligence
A Dichotomy Theorem for Learning Quantified Boolean Formulas
Machine Learning - Special issue: computational learning theory, COLT '97
Machine Learning
Machine Learning
A Unifying Framework for Tractable Constraints
CP '95 Proceedings of the First International Conference on Principles and Practice of Constraint Programming
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Some Dichotomy Theorems for Neural Learning Problems
The Journal of Machine Learning Research
The expressive rate of constraints
Annals of Mathematics and Artificial Intelligence
Maximum H-colourable subdigraphs and constraint optimization with arbitrary weights
Journal of Computer and System Sciences
Learning intersection-closed classes with signatures
Theoretical Computer Science
Hard constraint satisfaction problems have hard gaps at location 1
Theoretical Computer Science
Tractability and Learnability Arising from Algebras with Few Subpowers
SIAM Journal on Computing
Ruling out polynomial-time approximation schemes for hard constraint satisfaction problems
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
| Hi-index | 5.23 |
We consider the following classes of quantified formulas. Fix a set of basic relations called a basis. Take conjunctions of these basic relations applied to variables and constants in arbitrary ways. Finally, quantify existentially or universally some of the variables. We introduce some conditions on the basis that guarantee efficient learnability. Furthermore, we show that with certain restrictions on the basis the classification is complete. We introduce, as an intermediate tool, a link between this class of quantified formulas and some well-studied structures in Universal Algebra called clones. More precisely, we prove that the computational complexity of the learnability of these formulas is completely determined by a simple algebraic property of the basis of relations: their clone of polymorphisms. Finally, we use this technique to give a simpler proof of the already known dichotomy theorem over Boolean domains.