Polynomial-time inference of arbitrary pattern languages

Lange, Steffen; Wiehagen, Rolf

doi:10.1007/bf03037093

Cited by 121 publications

(74 citation statements)

References 7 publications

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“…Fortunately, Lange and Wiehagen [13] have designed a pattern language learner for finitely learning from good examples which completely avoids membership tests. Also, Lange and Wiehagen [13] have shown that for every pattern π there is a set of good examples of cardinality linear in |π| .…”

Section: Towards More Realistic Learning Scenariosmentioning

confidence: 99%

“…Also, Lange and Wiehagen [13] have shown that for every pattern π there is a set of good examples of cardinality linear in |π| .…”

Section: Towards More Realistic Learning Scenariosmentioning

confidence: 99%

“…In [21], we have dealt with the best-case, worst-case and average-case analysis of Lange and Wiehagen's [13] pattern language learning algorithm. The results obtained considerably improve Lange and Wiehagen's assertion concerning the minimal size of sets of good examples.…”

Section: Towards More Realistic Learning Scenariosmentioning

confidence: 99%

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Inductive Inference and Language Learning

Zeugmann

2006

Lecture Notes in Computer Science

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Section: Towards More Realistic Learning Scenariosmentioning

confidence: 99%

“…Also, Lange and Wiehagen [13] have shown that for every pattern π there is a set of good examples of cardinality linear in |π| .…”

Section: Towards More Realistic Learning Scenariosmentioning

confidence: 99%

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Inductive Inference and Language Learning

Zeugmann

2006

Lecture Notes in Computer Science

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“…The first polynomial-time algorithm for learning pattern languages was presented by Lange and Wiehagen [10].…”

Section: Introductionmentioning

confidence: 99%

Polynomial-Time Algorithms for Learning Typed Pattern Languages

Geilke

Zilles

2012

Language and Automata Theory and Applications

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Abstract. This article proposes polynomial-time algorithms for learning typed pattern languages-formal languages that are generated by patterns consisting of terminal symbols and typed variables. A string is generated by a typed pattern by substituting all variables with strings of terminal symbols that belong to the corresponding types. The algorithms presented consitute non-trivial generalizations of Lange and Wiehagen's efficient algorithm for learning patterns in which variables are not typed. This is achieved by defining type witnesses to impose structural conditions on the types used in the patterns. It is shown that Lange and Wiehagen's algorithm implicitly uses a special case of type witnesses. Moreover, the type witnesses for a typed pattern form characteristic sets whose size is linear in the length of the pattern; our algorithm, when processing any set of positive data containing such a characteristic set, will always generate a typed pattern equivalent to the target pattern. Thus our algorithms are of relevance to the area of grammatical inference, in which such characteristic sets are typically studied.

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“…In the sequel there has been a variety of profound studies (e.g. in [LW91], [WZ94], [RZ98], and many more) on the complexity of learning algorithms, consequences of different input data, efficient strategies for subclasses, and so on. Regarding E-pattern languages, however, appropriate approaches presumably need to be more sophisticated and therefore progress has been rather scarce.…”

Section: Introductionmentioning

confidence: 99%

A Discontinuity in Pattern Inference

Reidenbach

2004

Lecture Notes in Computer Science

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Abstract. This paper examines the learnability of a major subclass of E-pattern languages -also known as erasing or extended pattern languages -in Gold's learning model: We show that the class of terminal-free E-pattern languages is inferrable from positive data if the corresponding terminal alphabet consists of three or more letters. Consequently, the recently presented negative result for binary alphabets is unique.

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Polynomial-time inference of arbitrary pattern languages

Cited by 121 publications

References 7 publications

Inductive Inference and Language Learning

Inductive Inference and Language Learning

Polynomial-Time Algorithms for Learning Typed Pattern Languages

A Discontinuity in Pattern Inference

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