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
Learning Conjunctions of Horn Clauses
Machine Learning - Computational learning theory
Cryptographic limitations on learning Boolean formulae and finite automata
Journal of the ACM (JACM)
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
A dichotomy theorem for learning quantified Boolean formulas
COLT '97 Proceedings of the tenth annual conference on Computational learning theory
An efficient membership-query algorithm for learning DNF with respect to the uniform distribution
Journal of Computer and System Sciences
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
Constraints, consistency and closure
Artificial Intelligence
Boolean Formulas are Hard to Learn for most Gate Bases
ALT '99 Proceedings of the 10th International Conference on Algorithmic Learning Theory
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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 and we present an extension of this theorem to bases with infinite size.