MAT learners for tree series: an abstract data type and two realizations

Drewes, Frank; Högberg, Johanna; Maletti, Andreas

doi:10.1007/s00236-011-0135-x

Cited by 6 publications

(3 citation statements)

References 18 publications

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“…In [69], key properties of observation tables are captured in an abstract data type (ADT) for learning deterministic WTA. The authors show that the ADT can be realized as an observation tree in the sense of Kearns and Vazirani [110], which may reduce the algorithm's complexity considerably.…”

Section: The Minimal Adequate Teacher Model Matmentioning

confidence: 99%

Learning Tree Languages

Björklund

Fernau

2016

Topics in Grammatical Inference

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Tree languages have proved to be a versatile and rewarding extension of the classical notion of string languages. Many nice applications have been established over the years, in areas such as Natural Language Processing, Information Extraction, and Computational Biology. Although some properties of string languages transfer easily to the tree case, in particular for regular languages, several computational aspects turn out to be harder. It is therefore both of theoretical and of practical interest to investigate how far and in what ways Grammatical Inference algorithms developed for the string case are applicable to trees. This chapter surveys known results in this direction. We begin by recalling the basics of tree language theory. Then, the most popular learning scenarios and algorithms are presented. Several applications of Grammatical Inference of tree languages are reviewed in some detail. We conclude by suggesting a number of directions for future research.

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Section: The Minimal Adequate Teacher Model Matmentioning

confidence: 99%

Learning Tree Languages

Björklund

Fernau

2016

Topics in Grammatical Inference

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“…Lemma 6.2 proves the correctness of Algorithm 3 because the minimal deterministic fta for a given tree language is unique (up to isomorphism) [GS84, Theorem 2.11.12]. The run-time of our algorithm should be compared to the previously (asymptotically) fastest equivalence test for dwta of [DHM11]…”

Section: Minimizationmentioning

confidence: 99%

“…Secondly, we apply pushing to the problem of testing equivalence. The currently fastest algorithm [DHM11] for checking equivalence of two deterministic weighted tree automata M and M runs in time O |M | • |M | . It is well known that two minimal deterministic weighted tree automata M and M are equivalent if and only if they can be obtained from each other by a pushing operation (with proper pushing weights).…”

Section: Introductionmentioning

confidence: 99%

Pushing for weighted tree automata

Hanneforth¹,

Maletti²,

Quernheim³

2018

Logical Methods in Computer Science ; Volume 14

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A weight normalization procedure, commonly called pushing, is introduced for weighted tree automata (wta) over commutative semifields. The normalization preserves the recognized weighted tree language even for nondeterministic wta, but it is most useful for bottom-up deterministic wta, where it can be used for minimization and equivalence testing. In both applications a careful selection of the weights to be redistributed followed by normalization allows a reduction of the general problem to the corresponding problem for bottom-up deterministic unweighted tree automata. This approach was already successfully used by Mohri and Eisner for the minimization of deterministic weighted string automata. Moreover, the new equivalence test for two wta M and M runs in time O (|M | + |M |) log (|Q| + |Q |) , where Q and Q are the states of M and M , respectively, which improves the previously best run-time O |M | • |M | .

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On the Regularity and Learnability of Ordered DAG Languages

Björklund

Ericson

2017

Implementation and Application of Automata

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MAT learners for tree series: an abstract data type and two realizations

Cited by 6 publications

References 18 publications

Learning Tree Languages

Learning Tree Languages

Pushing for weighted tree automata

On the Regularity and Learnability of Ordered DAG Languages

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