A String Diagrammatic Axiomatisation of Finite-State Automata

We develop a fully diagrammatic approach to finite-state automata, based on reinterpreting their usual state-transition graphical representation as a two-dimensional syntax of string diagrams. In this setting, we are able to provide a complete equational theory for language equivalence, with two not...

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Detalles Bibliográficos
Autores principales: Piedeleu, Robin, Zanasi, Fabio
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7984119/
http://dx.doi.org/10.1007/978-3-030-71995-1_24
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author Piedeleu, Robin
Zanasi, Fabio
author_facet Piedeleu, Robin
Zanasi, Fabio
author_sort Piedeleu, Robin
collection PubMed
description We develop a fully diagrammatic approach to finite-state automata, based on reinterpreting their usual state-transition graphical representation as a two-dimensional syntax of string diagrams. In this setting, we are able to provide a complete equational theory for language equivalence, with two notable features. First, the proposed axiomatisation is finite— a result which is provably impossible for the one-dimensional syntax of regular expressions. Second, the Kleene star is a derived concept, as it can be decomposed into more primitive algebraic blocks.
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spelling pubmed-79841192021-03-23 A String Diagrammatic Axiomatisation of Finite-State Automata Piedeleu, Robin Zanasi, Fabio Foundations of Software Science and Computation Structures Article We develop a fully diagrammatic approach to finite-state automata, based on reinterpreting their usual state-transition graphical representation as a two-dimensional syntax of string diagrams. In this setting, we are able to provide a complete equational theory for language equivalence, with two notable features. First, the proposed axiomatisation is finite— a result which is provably impossible for the one-dimensional syntax of regular expressions. Second, the Kleene star is a derived concept, as it can be decomposed into more primitive algebraic blocks. 2021-03-23 /pmc/articles/PMC7984119/ http://dx.doi.org/10.1007/978-3-030-71995-1_24 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
Piedeleu, Robin
Zanasi, Fabio
A String Diagrammatic Axiomatisation of Finite-State Automata
title A String Diagrammatic Axiomatisation of Finite-State Automata
title_full A String Diagrammatic Axiomatisation of Finite-State Automata
title_fullStr A String Diagrammatic Axiomatisation of Finite-State Automata
title_full_unstemmed A String Diagrammatic Axiomatisation of Finite-State Automata
title_short A String Diagrammatic Axiomatisation of Finite-State Automata
title_sort string diagrammatic axiomatisation of finite-state automata
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7984119/
http://dx.doi.org/10.1007/978-3-030-71995-1_24
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