On the Expressiveness of Büchi Arithmetic

We show that the existential fragment of Büchi arithmetic is strictly less expressive than full Büchi arithmetic of any base, and moreover establish that its [Formula: see text] -fragment is already expressively complete. Furthermore, we show that regular languages of polynomial growth are definable...

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Autores principales: Haase, Christoph, Różycki, Jakub
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7984115/
http://dx.doi.org/10.1007/978-3-030-71995-1_16
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author Haase, Christoph
Różycki, Jakub
author_facet Haase, Christoph
Różycki, Jakub
author_sort Haase, Christoph
collection PubMed
description We show that the existential fragment of Büchi arithmetic is strictly less expressive than full Büchi arithmetic of any base, and moreover establish that its [Formula: see text] -fragment is already expressively complete. Furthermore, we show that regular languages of polynomial growth are definable in the existential fragment of Büchi arithmetic.
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spelling pubmed-79841152021-03-23 On the Expressiveness of Büchi Arithmetic Haase, Christoph Różycki, Jakub Foundations of Software Science and Computation Structures Article We show that the existential fragment of Büchi arithmetic is strictly less expressive than full Büchi arithmetic of any base, and moreover establish that its [Formula: see text] -fragment is already expressively complete. Furthermore, we show that regular languages of polynomial growth are definable in the existential fragment of Büchi arithmetic. 2021-03-23 /pmc/articles/PMC7984115/ http://dx.doi.org/10.1007/978-3-030-71995-1_16 Text en © The Author(s) 2021 Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
spellingShingle Article
Haase, Christoph
Różycki, Jakub
On the Expressiveness of Büchi Arithmetic
title On the Expressiveness of Büchi Arithmetic
title_full On the Expressiveness of Büchi Arithmetic
title_fullStr On the Expressiveness of Büchi Arithmetic
title_full_unstemmed On the Expressiveness of Büchi Arithmetic
title_short On the Expressiveness of Büchi Arithmetic
title_sort on the expressiveness of büchi arithmetic
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7984115/
http://dx.doi.org/10.1007/978-3-030-71995-1_16
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