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Learning deterministic DEC grammars is learning rational numbers

Summary: Learning deterministic DEC grammars is learning
rational numbers 
Pieter Adriaans.
Address: Department of Computer Science,
University of Amsterdam,
Kruislaan 419, 1098VA Amsterdam
Below I show that the class of strings that can be learned by a deter-
ministic DEC grammar is exactly the class of rational numbers between
0 and 1. I call this the class of semi-periodic or rational strings. Dynami-
cally Expanding Context (Dec) grammars were introduced by Kohonen in
order to model speech signals (Kohonen [1986]). They can be learned in
quadratic time in the size of the grammar. They have been used success-
fully in the automatic generation and analysis of music (Kohonen et al.
[1991], Adriaans and van Dungen [2001], Kohonen [1995]).
1 DEC grammars
Kohonen [1986] originally developed the idea of Dynamically Expanding Con-
text (DEC) grammars. DEC grammars are interesting because they are very
easy to learn (polynomial complexity) and they have interesting potential ap-


Source: Adriaans, Pieter - Instituut voor Informatica, Universiteit van Amsterdam


Collections: Computer Technologies and Information Sciences