 
Summary: Learning deterministic DEC grammars is learning
rational numbers
Pieter Adriaans.
Address: Department of Computer Science,
University of Amsterdam,
Kruislaan 419, 1098VA Amsterdam
pietera@science.uva.nl.
Abstract
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 semiperiodic 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
