Abstract

Several algorithms have been proposed to learn different subclasses of context-free grammars based on the idea generically called distributional learning. Those techniques have been applied to many formalisms richer than context-free grammars like multiple context-free grammars, simple contextfree tree grammars and others. The learning algorithms for those different formalisms are actually quite similar to each other. We in this paper give a uniform view on those algorithms.

Highlights

  • Approaches based on the idea generically called distributional learning have been making great success in the algorithmic learning of various subclasses of context-free grammars (CFGs) (Clark, 2010c; Yoshinaka, 2012)

  • Every grammar formalism for which distributional learning techniques have been proposed so far generate their languages through context-free derivation trees, whose nodes are labeled by production rules

  • We show that grammars with different distributional properties are learnable by standard distributional learning techniques if the formalism satisfies some conditions, which include polynomialtime decomposability of objects into contexts and Proceedings of the 14th Meeting on the Mathematics of Language (MoL 14), pages 87–98, Chicago, USA, July 25–26, 2015. c 2015 Association for Computational Linguistics substructures

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Summary

Introduction

Approaches based on the idea generically called distributional learning have been making great success in the algorithmic learning of various subclasses of context-free grammars (CFGs) (Clark, 2010c; Yoshinaka, 2012). Those techniques are applied to richer formalisms as well. In the CFG case, c is a string pair ⟨l, r⟩ and s is a string u and ⟨l, r⟩ ⊙ u = lur, which may correspond to a derivation I ⇒∗ lXr ⇒∗ lur where I is the initial symbol and X is a nonterminal symbol In richer formalisms those substructures and contexts may have richer structures, like tuples of strings or λ-terms. We discuss cases where we cannot enumerate all of the possible contexts and substructures

Σ-grammars
Context-substructure relation
Conditions to be distributionally learnable
Learning models
Learnable subclasses
Congruential grammars
Context-deterministic grammars
Combined approaches
Restricted cases
Extending learnable classes
Grammars with partial functions
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