Languages with Decidable Learning: A Meta-theorem

TL;DR

This paper introduces a meta-theorem connecting finite-aspect checkable languages to finite tree automata, enabling decidable learning for certain symbolic languages with syntactic restrictions.

Contribution

It defines finite-aspect checkable languages and provides a meta-theorem linking their evaluation programs to finite automata, facilitating decidable learning.

Findings

Characterization of languages with decidable learning

Development of a generic programming language for evaluation

Derivation of new decidable learning results

Abstract

We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined using a bounded amount of auxiliary information that is independent of expression size but depends on a fixed structure over which evaluation occurs. We introduce a generic programming language for writing programs that evaluate expression syntax trees, and we give a meta-theorem that connects such programs for finite-aspect checkable languages to finite tree automata, which allows us to derive new decidable learning results and decision procedures for several expression learning problems by writing programs in the programming language.