Even linear simple matrix languages: formal language properties and grammatical inference

We show that so-called deterministic even linear simple matrix grammars can be inferred in polynomial time using the query-based learner–teacher model (minimally adequate teacher-learning model) proposed by Angluin (Inform. and Comput. 75 (1987) 87) for learning deterministic regular languages. In t...

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Bibliographic Details
Published in:Theoretical computer science Vol. 289; no. 1; pp. 425 - 456
Main Author: Fernau, Henning
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 23.10.2002
Elsevier
Subjects:
Algebra
Applied sciences
Computer science; control theory; systems
Control language
Exact sciences and technology
Formal languages
Grammatical inference
Khabbaz hierarchies
Language characterizations
Language theory and syntactical analysis
Learning
Linear and multilinear algebra, matrix theory
MAT model
Mathematics
Sciences and techniques of general use
Simple matrix grammars
Theoretical computing
Europe
Berlin
Germany
Learning
MAT model
Formal languages
Control language
Khabbaz hierarchies
Simple matrix grammars
Language characterizations
Grammatical inference
Linear grammar
Polynomial
Inclusion
Language theory
Decidability
Closure
Query
Algorithmics
Process
Image
Properties
Knowledge
Characterization
Learning systems
Universal grammar
Control
Relation
1995
1994
Language class
1992
Computer
Language recognition
Formal language
Simple matrix grammar
Normal form
Inference
Regular language
Pattern recognition
Polynomial time
1987
Computer science
Image analysis
Models
Computer system
Application
Artificial intelligence
1988
Deterministic language
ISSN:0304-3975, 1879-2294
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Summary:We show that so-called deterministic even linear simple matrix grammars can be inferred in polynomial time using the query-based learner–teacher model (minimally adequate teacher-learning model) proposed by Angluin (Inform. and Comput. 75 (1987) 87) for learning deterministic regular languages. In this way, we extend the class of efficiently learnable languages beyond both the even linear languages and the even equal matrix languages (Pattern Recognition 21 (1988) 55; Proc. 2nd Internat. Colloq. on Grammatical Inference (ICGI-94): Grammatical Inference and Applications, Lecture Notes in Computer Science/Lecture Notes in Artificial Intelligence, vol. 862, Springer, Berlin, 1994, p. 38; Inform. Process. Lett. 28 (1988) 193; Technical Report IIAS-RR-93-6E, Fujitsu Laboratories, 1992; Parallel Image Analysis, ICPIA’92, Lecture Notes in Computer Science, vol. 652, Springer, Berlin, 1992, p. 274; Inform. and Comput. 123 (1995) 138; Algorithmic Learning for Knowledge-Based Systems, Lecture Notes in Computer Science/Lecture Notes in Artificial Intelligence, Springer, Berlin, 1995, p. 317). Moreover, we investigate formal language properties of even linear simple matrix languages and related language classes. More precisely, we discuss characterizations, (proper) inclusion relations, closure properties and decidability questions. This way, we also show that, in a certain sense, the idea of iterating the control language approach for learning purposes, as undertook by Takada (1995), could be seen as a special case of using deterministic even linear simple matrix grammars as basic and uniform learning target.
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ISSN:0304-3975
1879-2294
DOI:10.1016/S0304-3975(01)00313-9