Safe Language Generation in the Limit

TL;DR

This paper provides a theoretical framework for safe language generation, showing its fundamental difficulty and establishing that safe identification is impossible, with some cases being tractable.

Contribution

It formalizes safe language identification and generation within the learning in the limit paradigm, proving their computational hardness.

Findings

Safe language identification is impossible.

Safe language generation is at least as hard as language identification.

Some cases of safe language generation are tractable.

Abstract

Recent results in learning a language in the limit have shown that, although language identification is impossible, language generation is tractable. As this foundational area expands, we need to consider the implications of language generation in real-world settings. This work offers the first theoretical treatment of safe language generation. Building on the computational paradigm of learning in the limit, we formalize the tasks of safe language identification and generation. We prove that under this model, safe language identification is impossible, and that safe language generation is at least as hard as (vanilla) language identification, which is also impossible. Last, we discuss several intractable and tractable cases.