On the complexity of inductive inference
Information and Control
Pattern languages are not learnable
COLT '90 Proceedings of the third annual workshop on Computational learning theory
Learning pattern languages from a single initial example and from queries
COLT '88 Proceedings of the first annual workshop on Computational learning theory
A polynomial-time algorithm for learning k-variable pattern languages from examples
COLT '89 Proceedings of the second annual workshop on Computational learning theory
Learning string patterns and tree patterns from examples
Proceedings of the seventh international conference (1990) on Machine learning
Polynomial-time inference of arbitrary pattern languages
New Generation Computing - Selected papers from the international workshop on algorithmic learning theory,1990
Types of monotonic language learning and their characterization
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Characterizations of monotonic and dual monotonic language learning
Information and Computation
Incremental learning from positive data
Journal of Computer and System Sciences
Learning unions of tree patterns using queries
Theoretical Computer Science - Special issue on algorithmic learning theory
Concrete Math
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
Algorithmic Learning for Knowledge-Based Systems, GOSLER Final Report
MDL learning of unions of simple pattern languages from positive examples
EuroCOLT '95 Proceedings of the Second European Conference on Computational Learning Theory
Monotonic Versus Nonmonotonic Language Learning
Proceedings of the Second International Workshop on Nonmonotonic and Inductive Logic
Formal languages and their relation to automata
Formal languages and their relation to automata
Learning one-variable pattern languages in linear average time
COLT' 98 Proceedings of the eleventh annual conference on Computational learning theory
On the learnability of recursively enumerable languages from good examples
Theoretical Computer Science
Theoretical Computer Science
Stochastic Finite Learning of the Pattern Languages
Machine Learning
On learning unions of pattern languages and tree patterns in the mistake bound model
Theoretical Computer Science
SAGA '01 Proceedings of the International Symposium on Stochastic Algorithms: Foundations and Applications
From Computational Learning Theory to Discovery Science
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
ALT '99 Proceedings of the 10th International Conference on Algorithmic Learning Theory
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
Inductive inference and language learning
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
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The present paper deals with the best‐case, worst‐case and average‐case behavior of Lange and Wiehagen’s (1991) pattern language learning algorithm with respect to its total learning time. Pattern languages have been introduced by Angluin (1980) and are defined as follows: Let \mathcal{A} = \{ 0,1,\dots\} be any non‐empty finite alphabet containing at least two elements. Furthermore, let X= \{x_i\mid i\in \mathbb{N}\} be an infinite set of variables such that \mathcal{A} \cap X = \emptyset. Patterns are non‐empty strings over \mathcal{A} \cup X. L(\pi), the language generated by pattern \pi, is the set of strings which can be obtained by substituting non‐null strings from \mathcal{A}^\ast for the variables of the pattern \pi. Lange and Wiehagen’s (1991) algorithm learns the class of all pattern languages in the limit from text. We analyze this algorithm with respect to its total learning time behavior, i.e., the overall time taken by the algorithm until convergence. For every pattern \pi containing k different variables it is shown that the total learning time is \mathrm{O}(\vert \pi\vert ^2 \log_{\vert \mathcal{A}\vert } (\vert \mathcal{A}\vert + k)) in the best‐case and unbounded in the worst‐case. Furthermore, we estimate the expectation of the total learning time. In particular, it is shown that Lange and Wiehagen’s algorithm possesses an expected total learning time of \mathrm{O}(2^kk^2\vert \pi\vert ^2\log_{\vert \mathcal{A}\vert }(k \vert \mathcal{A}\vert )) with respect to the uniform distribution.