TY - JOUR

T1 - Polynomial-time identification of very simple grammars from positive data

AU - Yokomori, Takashi

N1 - Funding Information:
This work is supported in part by Grants-in-Aid for Scienti%c Research Nos. 03245104 and 04229105 from the Ministry of Education, Science, Sports and Culture, Japan.

PY - 2003/4/4

Y1 - 2003/4/4

N2 - 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.

AB - 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.

KW - Identification in the limit from positive data

KW - Polynomial-time learning

KW - Very simple grammars

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U2 - 10.1016/S0304-3975(02)00423-1

DO - 10.1016/S0304-3975(02)00423-1

M3 - Article

AN - SCOPUS:0037418708

VL - 298

SP - 179

EP - 206

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 1

ER -