A proof theory of (omega-)context-free languages, via non-wellfounded proofs
Abstract
We investigate the proof theory of regular expressions with fixed points, construed as a notation for (omega-)context-free grammars. Starting with a hypersequential system for regular expressions due to Das and Pous, we define its extension by least fixed points and prove soundness and completeness of its non-wellfounded proofs for the standard language model. From here we apply proof-theoretic techniques to recover an infinitary axiomatisation of the resulting equational theory, complete for inclusions of context-free languages. Finally, we extend our syntax by greatest fixed points, now computing omega-context-free languages. We show the soundness and completeness of the corresponding system using a mixture of proof-theoretic and game-theoretic techniques.
Cite
@article{arxiv.2404.16231,
title = {A proof theory of (omega-)context-free languages, via non-wellfounded proofs},
author = {Anupam Das and Abhishek De},
journal= {arXiv preprint arXiv:2404.16231},
year = {2024}
}
Comments
24 pages, 5 figures