A proof theory of (omega-)context-free languages, via non-wellfounded proofs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929327145222144 |
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| author | Das, Anupam De, Abhishek |
| author_facet | Das, Anupam De, Abhishek |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16231 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A proof theory of (omega-)context-free languages, via non-wellfounded proofs Das, Anupam De, Abhishek Logic in Computer Science Logic 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. |
| title | A proof theory of (omega-)context-free languages, via non-wellfounded proofs |
| topic | Logic in Computer Science Logic |
| url | https://arxiv.org/abs/2404.16231 |