Logic for Unambiguous Context-Free Languages

TL;DR

This paper provides a logical characterization of unambiguous context-free languages, linking descriptive complexity with language theory and establishing a new connection between undecidable problems.

Contribution

It introduces a logical framework for unambiguous context-free languages using a fragment of logic based on implicit definability, extending prior work on context-free languages.

Findings

Established a logical characterization for unambiguous context-free languages.

Connected undecidable problems in logic and language theory.

Extended the understanding of descriptive complexity in formal languages.

Abstract

We give in this paper a logical characterization for unambiguous Context Free Languages, in the vein of descriptive complexity. A fragment of the logic characterizing context free languages given by Lautemann, Schwentick and Th\'erien [18] based on implicit definability is used for this aim. We obtain a new connection between two undecidable problems, a logical one and a language theoretical one.