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arXiv · 2411.08523

The Word Problem for $(\omega - 1)$-Terms over $\mathrm{DAb}$

Jorge Almeida·Manfred Kufleitner·Jan Philipp Wächter
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Abstract

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 $(\omega - 1)$-terms, this normal form is computable, which yields an algorithm for the word problem for $(\omega - 1)$-terms of $\boldsymbol{\mathrm{DAb}}$.

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Jorge Almeida, Manfred Kufleitner, Jan Philipp Wächter. 2024-11-13. The Word Problem for $(\omega - 1)$-Terms over $\mathrm{DAb}$. https://arxiv.org/abs/2411.08523

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