Language Identification with Succinct Machine-Independent Traces

2026-07-14

AI Summary

This work addresses the problem of achieving learnability in the limit for arbitrary classes of languages without relying on underlying automaton-based generative models. The authors propose a novel trajectory construction method that operates directly on the intrinsic structure of the target language, eschewing any presupposed computational model. Crucially, the method confines the size of the alphabet used in the constructed trajectories to a linear bound relative to that of the original language. Within the Gold–Angluin framework of identification in the limit, this approach enables effective learnability of arbitrary language classes through succinct, finitely labeled trajectories. It thereby establishes, for the first time, a model-agnostic mechanism for trajectory construction that is intrinsically tied to the language itself.

Abstract

Motivated by the power of large language models, there has been renewed interest in the Gold-Angluin model of language identification in the limit, with an eye toward variants of the model that might overcome the negative results for its original formulation. Recent papers on this question have proposed looking at computational traces and annotations of training strings as a source of additional power for a learner, reflecting empirical regularities such as the way that commented source code is easier to learn from than arbitrary source code, and text annotated with algorithmically generated chain-of-thought tokens can be easier to learn from than the raw text itself. This recent work has shown positive results for language identification in the presence of such computational traces, but the traces in these positive results come from explicit automata-theoretic machine models that generate the language, where the underlying vocabulary of tokens for the traces is very large. In this paper, we address two fundamental issues left open by this line of work: can we achieve positive results with traces that use only a small alphabet, and can we define traces directly from the language itself, without requiring an underlying machine model that generates it? We establish positive results for both of these questions: for an arbitrary collection of languages, we show how to define computational traces that enable identification in the limit, using an alphabet of tokens that is linear in the size of the alphabet that the languages are defined over, and independent of any other properties of the languages.

Problem

• language identification
• computational traces
• machine-independent
• succinct representation
• Gold-Angluin model

Innovation

• language identification
• computational traces
• machine-independent
• succinct alphabet
• identification in the limit