A proof theory of (omega-)context-free languages, via non-wellfounded proofs
<|reference_start|>A proof theory of (omega-)context-free languages, via non-wellfounded proofs: 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.<|reference_end|>
@article{das2024a,
    title={A proof theory of (omega-)context-free languages, via non-wellfounded
  proofs},
    author={Anupam Das, Abhishek De},
    journal={arXiv preprint arXiv:2404.16231},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.16231},
    primaryClass={cs.LO math.LO}
}