A substitution lemma for multiple context-free languages
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917527383179264 |
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| author | Duncan, Andrew Elder, Murray Frenkel, Lisa Lyu, Mengfan |
| author_facet | Duncan, Andrew Elder, Murray Frenkel, Lisa Lyu, Mengfan |
| contents | We present a necessary condition for an infinite language to be multiple context-free, which we call a Substitution Lemma. We apply it to show a sample selection of languages are not multiple context-free, including the word problem of the group $F_2\times F_2$. We also show that groups with multiple context-free word problem have decidable rational subset membership problem.
Our result contrasts with previous work showing that the standard pumping lemma for context-free languages cannot be generalised to multiple context-free languages, and that weak variants of generalised Ogden's lemma do not apply to multiple context-free languages. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02117 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A substitution lemma for multiple context-free languages Duncan, Andrew Elder, Murray Frenkel, Lisa Lyu, Mengfan Formal Languages and Automata Theory Group Theory 20E06, 68Q45 We present a necessary condition for an infinite language to be multiple context-free, which we call a Substitution Lemma. We apply it to show a sample selection of languages are not multiple context-free, including the word problem of the group $F_2\times F_2$. We also show that groups with multiple context-free word problem have decidable rational subset membership problem. Our result contrasts with previous work showing that the standard pumping lemma for context-free languages cannot be generalised to multiple context-free languages, and that weak variants of generalised Ogden's lemma do not apply to multiple context-free languages. |
| title | A substitution lemma for multiple context-free languages |
| topic | Formal Languages and Automata Theory Group Theory 20E06, 68Q45 |
| url | https://arxiv.org/abs/2509.02117 |