Distributional Learning of Some Context-Free Languages with a Minimally Adequate Teacher

Angluin showed that the class of regular languages could be learned from a Minimally Adequate Teacher (mat) providing membership and equivalence queries. Clark and Eyraud (2007) showed that some context free grammars can be identified in the limit from positive data alone by identifying the congruence classes of the language. In this paper we consider learnability of context free languages using a MAT. We show that there is a natural class of context free languages, that includes the class of regular languages, that can be polynomially learned from a MAT, using an algorithm that is an extension of Angluin's LSTAR algorithm.

[1]  Alexander Clark,et al.  Polynomial Identification in the Limit of Substitutable Context-free Languages , 2005 .

[2]  Sampath Kannan,et al.  A Quasi-Polynomial-Time Algorithm for Sampling Words from a Context-Free Language , 1997, Inf. Comput..

[3]  Dana Angluin,et al.  Inference of Reversible Languages , 1982, JACM.

[4]  Seymour Ginsburg,et al.  The mathematical theory of context free languages , 1966 .

[5]  D. Angluin.  Negative Results for Equivalence Queries , 1990, Machine Learning.

[6]  Géraud Sénizergues,et al.  The Equivalence and Inclusion Problems for NTS Languages , 1985, J. Comput. Syst. Sci..

[7]  Dominique Estival,et al.  The Tenjinno Machine Translation Competition , 2006, ICGI.

[8]  Luc Boasson,et al.  NTS Languages Are Deterministic and Congruential , 1985, J. Comput. Syst. Sci..

[9]  Colin de la Higuera,et al.  A bibliographical study of grammatical inference , 2005, Pattern Recognit..

[10]  Yuji Takada.  Grammatical Interface for Even Linear Languages Based on Control Sets , 1988, Inf. Process. Lett..

[11]  E. Mark Gold,et al.  Complexity of Automaton Identification from Given Data , 1978, Inf. Control..

[12]  Ryo Yoshinaka,et al.  Identification in the Limit of k, l-Substitutable Context-Free Languages , 2008, ICGI.

[13]  Colin de la Higuera,et al.  Zulu: An Interactive Learning Competition , 2009, FSMNLP.

[14]  Joost Engelfriet.  Deciding the NTS Property of Context-Free Grammars , 1994, Results and Trends in Theoretical Computer Science.

[15]  Menno van Zaanen,et al.  The Omphalos Context-Free Grammar Learning Competition , 2004, ICGI.

[16]  Takashi Yokomori,et al.  Polynomial-time MAT Learning of C-Deterministic Context-free Grammars , 1993 .

[17]  Grzegorz Rozenberg,et al.  Results and Trends in Theoretical Computer Science , 1994, Lecture Notes in Computer Science.

[18]  Amaury Habrard,et al.  A Polynomial Algorithm for the Inference of Context Free Languages , 2008, ICGI.

[19]  Dana Angluin,et al.  Learning Regular Sets from Queries and Counterexamples , 1987, Inf. Comput..

[20]  Alexander Clark,et al.  A Learnable Representation for Syntax Using Residuated Lattices , 2009, FG.