Equational Theories of Scattered and Countable Series-Parallel Posets

In this paper we consider two classes of posets labeled over an alphabet A. The class [Formula: see text] is built from the letters and closed under the operations of series finite, [Formula: see text] and [Formula: see text] products, and finite parallel product. In the class [Formula: see text], [...

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Autores principales: Amazigh, Amrane, Bedon, Nicolas
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7247904/
http://dx.doi.org/10.1007/978-3-030-48516-0_1
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author Amazigh, Amrane
Bedon, Nicolas
author_facet Amazigh, Amrane
Bedon, Nicolas
author_sort Amazigh, Amrane
collection PubMed
description In this paper we consider two classes of posets labeled over an alphabet A. The class [Formula: see text] is built from the letters and closed under the operations of series finite, [Formula: see text] and [Formula: see text] products, and finite parallel product. In the class [Formula: see text], [Formula: see text] and [Formula: see text] products are replaced by [Formula: see text] and [Formula: see text] powers. We prove that [Formula: see text] and [Formula: see text] are freely generated in their respective natural varieties of algebras [Formula: see text] and [Formula: see text], and that the equational theory of [Formula: see text] is decidable.
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spelling pubmed-72479042020-05-26 Equational Theories of Scattered and Countable Series-Parallel Posets Amazigh, Amrane Bedon, Nicolas Developments in Language Theory Article In this paper we consider two classes of posets labeled over an alphabet A. The class [Formula: see text] is built from the letters and closed under the operations of series finite, [Formula: see text] and [Formula: see text] products, and finite parallel product. In the class [Formula: see text], [Formula: see text] and [Formula: see text] products are replaced by [Formula: see text] and [Formula: see text] powers. We prove that [Formula: see text] and [Formula: see text] are freely generated in their respective natural varieties of algebras [Formula: see text] and [Formula: see text], and that the equational theory of [Formula: see text] is decidable. 2020-05-26 /pmc/articles/PMC7247904/ http://dx.doi.org/10.1007/978-3-030-48516-0_1 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Amazigh, Amrane
Bedon, Nicolas
Equational Theories of Scattered and Countable Series-Parallel Posets
title Equational Theories of Scattered and Countable Series-Parallel Posets
title_full Equational Theories of Scattered and Countable Series-Parallel Posets
title_fullStr Equational Theories of Scattered and Countable Series-Parallel Posets
title_full_unstemmed Equational Theories of Scattered and Countable Series-Parallel Posets
title_short Equational Theories of Scattered and Countable Series-Parallel Posets
title_sort equational theories of scattered and countable series-parallel posets
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7247904/
http://dx.doi.org/10.1007/978-3-030-48516-0_1
work_keys_str_mv AT amazighamrane equationaltheoriesofscatteredandcountableseriesparallelposets
AT bedonnicolas equationaltheoriesofscatteredandcountableseriesparallelposets

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