Polynomial-time identification of very simple grammars from positive data

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Abstract

This paper concerns a subclass of simple deterministic grammars, called very simple grammars, and studies the problem of identifying the subclass in the limit from positive data. The class of very simple languages forms a proper subclass of simple deterministic languages and is incomparable to the class of regular languages. This class of languages is also known as the class of left Szilard languages of context-free grammars. After providing some properties of very simple languages, we show that the class of very simple grammars is polynomial-time identifiable in the limit from positive data in the following sense. That is, we show that there effectively exists an algorithm that, given a target very simple grammar G* over alphabet Σ, identifies a very simple grammar G equivalent to G* in the limit from positive data, satisfying the property that the time for updating a conjecture is bounded by O(m), and the total number of prediction errors made by the algorithm is bounded by O(n), where n is the size of G*, m = Max{N|Σ|+1,|Σ|3} and N is the total length of all positive data provided.

Original languageEnglish
Pages (from-to)179-206
Number of pages28
JournalTheoretical Computer Science
Volume298
Issue number1
DOIs
Publication statusPublished - 2003 Apr 4

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Keywords

  • Identification in the limit from positive data
  • Polynomial-time learning
  • Very simple grammars

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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