Work

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

Year: 2024

Type: preprint

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

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2411.08523

Authors: Almeida, Jorge, Kufleitner, Manfred, Wächter, Jan Philipp

Institutions: Universidade do Porto, Centro de Matemática, University of Stuttgart

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Universidade do Porto, Engineering and Physical Sciences Research Council, Fundação para a Ciência e a Tecnologia, Centro de Matemática Universidade do Porto

Awards: Centro de Matemática da Universidade do Porto, Special Inverse Monoids: Geometry, Structure & Algorithms, G5341562090, Centro de Matemática da Universidade do Porto, G5632191363, Algebraische Entscheidungsprobleme über der Aktivitätshierarchie von Automatenstrukturen, G8367123964

OpenAlex ID: W4404407763

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