The Word Problem for $(ω- 1)$-Terms over $\mathrm{DAb}$
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| Format: | Preprint |
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2024
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| _version_ | 1866912119242358784 |
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| author | Almeida, Jorge Kufleitner, Manfred Wächter, Jan Philipp |
| author_facet | Almeida, Jorge Kufleitner, Manfred Wächter, Jan Philipp |
| contents | We give a ranker-based description using finite-index congruences for the variety $\boldsymbol{\mathrm{DAb}}$ of finite monoids whose regular $\mathcal{D}$-classes form Abelian groups. This combinatorial description yields a normal form for general pseudowords over $\boldsymbol{\mathrm{DAb}}$. For $(ω- 1)$-terms, this normal form is computable, which yields an algorithm for the word problem for $(ω- 1)$-terms of $\boldsymbol{\mathrm{DAb}}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_08523 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Word Problem for $(ω- 1)$-Terms over $\mathrm{DAb}$ Almeida, Jorge Kufleitner, Manfred Wächter, Jan Philipp Formal Languages and Automata Theory Group Theory 20M07, 20M35, 68Q45 F.4.3 We give a ranker-based description using finite-index congruences for the variety $\boldsymbol{\mathrm{DAb}}$ of finite monoids whose regular $\mathcal{D}$-classes form Abelian groups. This combinatorial description yields a normal form for general pseudowords over $\boldsymbol{\mathrm{DAb}}$. For $(ω- 1)$-terms, this normal form is computable, which yields an algorithm for the word problem for $(ω- 1)$-terms of $\boldsymbol{\mathrm{DAb}}$. |
| title | The Word Problem for $(ω- 1)$-Terms over $\mathrm{DAb}$ |
| topic | Formal Languages and Automata Theory Group Theory 20M07, 20M35, 68Q45 F.4.3 |
| url | https://arxiv.org/abs/2411.08523 |