Communications of the ACM
Systems that learn: an introduction to learning theory for cognitive and computer scientists
Systems that learn: an introduction to learning theory for cognitive and computer scientists
On the complexity of inductive inference
Information and Control
Identification of pattern languages from examples and queries
Information and Computation
A note on the two-variable pattern-finding problem
Journal of Computer and System Sciences
Deterministic simulation of idealized parallel computers on more realistic ones
SIAM Journal on Computing
Prudence and other conditions on formal language learning
Information and Computation
A polynomial-time algorithm for learning k-variable pattern languages from examples
COLT '89 Proceedings of the second annual workshop on Computational learning theory
Polynomial-time inference of arbitrary pattern languages
New Generation Computing - Selected papers from the international workshop on algorithmic learning theory,1990
Efficient PRAM simulation on a distributed memory machine
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
An introduction to parallel algorithms
An introduction to parallel algorithms
Annals of Mathematics and Artificial Intelligence
Machine Learning
Machine Learning
Polynomial Time Inference of Extended Regular Pattern Languages
Proceedings of RIMS Symposium on Software Science and Engineering
Inclusion is Undecidable for Pattern Languages
ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
Polynomial Time Inference of General Pattern Languages
STACS '84 Proceedings of the Symposium of Theoretical Aspects of Computer Science
The Relation of Two Patterns with Comparable Languages
STACS '88 Proceedings of the 5th Annual Symposium on Theoretical Aspects of Computer Science
Algorithmic Learning for Knowledge-Based Systems, GOSLER Final Report
A Guided Tour Across the Boundaries of Learning Recursive Languages
Algorithmic Learning for Knowledge-Based Systems, GOSLER Final Report
Inductive Inference of Unbounded Unions of Pattern Languages from Positive Data
ALT '96 Proceedings of the 7th International Workshop on Algorithmic Learning Theory
Monotonic and Nonmonotonic Inductive Inference of Functions and Patterns
Proceedings of the 1st International Workshop on Nonmonotonic and Inductive Logic
Parallelism in random access machines
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Formal languages and their relation to automata
Formal languages and their relation to automata
SAGA '01 Proceedings of the International Symposium on Stochastic Algorithms: Foundations and Applications
From learning in the limit to stochastic finite learning
Theoretical Computer Science - Algorithmic learning theory
Learning a subclass of regular patterns in polynomial time
Theoretical Computer Science - Algorithmic learning theory
Learning indexed families of recursive languages from positive data: A survey
Theoretical Computer Science
Developments from enquiries into the learnability of the pattern languages from positive data
Theoretical Computer Science
Regular patterns, regular languages and context-free languages
Information Processing Letters
Learnability of automatic classes
Journal of Computer and System Sciences
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A pattern is a finite string of constant and variable symbols. The langauge generated by a pattern is the set of all strings of constant symbols which can be obtained from the pattern by substituting non-empty strings for variables. We study the learnability of one-variable pattern languages in the limit with respect to the update time needed for computing a new single hypothesis and the expected total learning time taken until convergence to a correct hypothesis. Our results are as follows. First, we design a consistent and set-driven learner that, using the concept of descriptive patterns, achieves update time O(n2logn), where n is the size of the input sample. The best previously known algorithm for computing descriptive one-variable patterns requires time O(n4logn) (cf. Angluin, J. Comput. Systems Sci. 21 (1) (1980) 46-62). Second, we give a parallel version of this algorithm that requires time O(logn) and O(n3/logn) processors on an EREW-PRAM. Third, using a modified version of the sequential algorithm as a subroutine, we devise a learning algorithm for one-variable patterns whose expected total learning time is O(l2logl) provided that sample strings are drawn from the target language according to a probability distribution with expected string length l. The probability distribution must be such that strings of equal length have equal probability, but can be arbitrary otherwise. Thus, we establish the first algorithm for learning one-variable pattern languages having an expected total learning time that provably differs from the update time by a constant factor only. Finally, we show how the algorithm for descriptive one-variable patterns can be used for learning one-variable patterns with a polynomial number of superset queries with respect to the one-variable patterns as query language.