Communications of the ACM
Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
Computational limitations on learning from examples
Journal of the ACM (JACM)
Crytographic limitations on learning Boolean formulae and finite automata
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Prediction-preserving reducibility
Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
PAC-learnability of determinate logic programs
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
The Utility of Knowledge in Inductive Learning
Machine Learning
Inverting implication with small training sets
ECML-94 Proceedings of the European conference on machine learning on Machine Learning
Flattening and Saturation: Two Representation Changes for Generalization
Machine Learning - Special issue on evaluating and changing representation
Recovering software specifications with inductive logic programming
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
The Learnability of Description Logics with Equality Constraints
Machine Learning - Special issue on computational learning theory, COLT'92
Pac-learning nondeterminate clauses
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Inducing deterministic Prolog parsers from treebanks: a machine learning approach
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
A Methodology for LISP Program Construction from Examples
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Learning Logical Definitions from Relations
Machine Learning
Learning Conjunctive Concepts in Structural Domains
Machine Learning
Some Lower Bounds for the Computational Complexity of Inductive Logic Programming
ECML '93 Proceedings of the European Conference on Machine Learning
ECML '93 Proceedings of the European Conference on Machine Learning
Background Knowledge and Declarative Bias in Inductive Concept Learning
AII '92 Proceedings of the International Workshop on Analogical and Inductive Inference
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Pac-learning recursive logic programs: efficient algorithms
Journal of Artificial Intelligence Research
Learning logic programs by using the product homomorphism method
COLT '97 Proceedings of the tenth annual conference on Computational learning theory
Learning first order universal Horn expressions
COLT' 98 Proceedings of the eleventh annual conference on Computational learning theory
Learning atomic formulas with prescribed properties
COLT' 98 Proceedings of the eleventh annual conference on Computational learning theory
Hardness Results for Learning First-Order Representations and Programming by Demonstration
Machine Learning - Special issue on the ninth annual conference on computational theory (COLT '96)
Learning Function-Free Horn Expressions
Machine Learning - The Eleventh Annual Conference on computational Learning Theory
Scaling Up Inductive Logic Programming by Learning from Interpretations
Data Mining and Knowledge Discovery
Learning closed horn expressions
Information and Computation
Mind change complexity of learning logic programs
Theoretical Computer Science
Mind Change Complexity of Learning Logic Programs
EuroCOLT '99 Proceedings of the 4th European Conference on Computational Learning Theory
Learning Range Restricted Horn Expressions
EuroCOLT '99 Proceedings of the 4th European Conference on Computational Learning Theory
Logical Aspects of Several Bottom-Up Fittings
ALT '98 Proceedings of the 9th International Conference on Algorithmic Learning Theory
On the Hardness of Learning Acyclic Conjunctive Queries
ALT '00 Proceedings of the 11th International Conference on Algorithmic Learning Theory
A New Algorithm for Learning Range Restricted Horn Expressions
ILP '00 Proceedings of the 10th International Conference on Inductive Logic Programming
Prediction-hardness of acyclic conjunctive queries
Theoretical Computer Science - Algorithmic learning theory (ALT 2000)
Generalization of clauses under implication
Journal of Artificial Intelligence Research
Pac-learning recursive logic programs: efficient algorithms
Journal of Artificial Intelligence Research
Relational learning for NLP using linear threshold elements
IJCAI'99 Proceedings of the 16th international joint conference on Artificial intelligence - Volume 2
Relational learning via propositional algorithms: an information extraction case study
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 2
The complexity of theory revision
Artificial Intelligence
Learning with feature description logics
ILP'02 Proceedings of the 12th international conference on Inductive logic programming
Proceedings of the 15th International Conference on Database Theory
ACM Transactions on Database Systems (TODS) - Invited papers issue
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In a companion paper it was shown that the class of constant-depth determinate k-ary recursive clauses is efficiently learnable. In this paper we present negative results showing that any natural generalization of this class is hard to learn in Valiant's model of paclearnability. In particular, we show that the following program classes are cryptographically hard to learn: programs with an unbounded number of constant-depth linear recursive clauses; programs with one constant-depth determinate clause containing an unbounded number of recursive calls; and programs with one linear recursive clause of constant locality. These results immediately imply the non-learnability of any more general class of programs. We also show that learning a constant-depth determinate program with either two linear recursive clauses or one linear recursive clause and one non-recursive clause is as hard as learning boolean DNF. Together with positive results from the companion paper, these negative results establish a boundary of efficient learnability for recursive function-free clauses.