Paper Info
Title
Language Learning From Texts: Degrees of Instrinsic Complexity and Their Characterizations
Abstract
This paper deals with two problems: 1) what makes languages to be learnable in the limit by natural strategies of varying hardness; 2) what makes classes of languages to be the hardest ones to learn. To quantify hardness of learning, we use intrinsic complexity based on reductions between learning problems. Two types of reductions are considered: weak reductions mapping texts (representations of languages) to texts, and strong reductions mapping languages to languages. For both types of reductions, characterizations of com- plete (hardest) classes in terms of their algorithmic and topological potentials have been obtained. To characterize the strong complete degree, we discovered a new and natural complete class capable of \coding" any learning problem using density of the set of rational numbers. We have also discovered and characterized rich hierarchies of degrees of com- plexity based on \core" natural learning problems. The classes in these hierarchies contain \multidimensional" languages, where the information learned from one dimension aids to learn other dimensions. In one formalization of this idea, the grammars learned from the dimensions 1; 2; : : : ; k specify the \subspace" for the dimension k + 1, while the learning strategy for every dimension is predened. In our other formalization, a \pattern" learned from the dimension k species the learning strategy for the dimension k + 1. A number of open problems is discussed.
Year
DOI
Venue
2000
10.1006/jcss.2001.1759
Journal of Computer and System Sciences
Keywords
DocType
Volume
language learning,instrinsic complexity,coding,computer languages
Conference
63
Issue
ISSN
ISBN
3
Journal of Computer and System Sciences
1-55860-703-X
Citations 
PageRank 
References 
11
0.62
20
Authors
3
Name
Order
Citations
PageRank
Sanjay Jain11647177.87
Efim Kinber242144.95
Rolf Wiehagen3835105.73