Learning without Coding

Iterative learning is a model of language learning from positive data, due to Wiehagen. When compared to a learner in Gold’s original model of language learning from positive data, an iterative learner can be thought of as

memory-limited

. However, an iterative learner can memorize

some

input elements by

coding

them into the syntax of its hypotheses. A main concern of this paper is: to what extent are such coding tricks

necessary

?

One means of preventing

some

such coding tricks is to require that the hypothesis space used be free of redundancy, i.e., that it be 1-1. By extending a result of Lange & Zeugmann, we show that many interesting and non-trivial classes of languages can be iteratively identified in this manner. On the other hand, we show that there exists a class of languages that can

not

be iteratively identified using any 1-1 effective numbering as the hypothesis space.

We also consider an iterative-like learning model in which the computational component of the learner is modeled as an

enumeration operator

, as opposed to a partial computable function. In this new model, there are no hypotheses, and, thus, no syntax in which the learner can encode what elements it has or has not yet seen. We show that there exists a class of languages that

can

be identified under this new model, but that can

not

be iteratively identified. On the other hand, we show that there exists a class of languages that can

not

be identified under this new model, but that

can

be iteratively identified using a Friedberg numbering as the hypothesis space.