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The Polynomial Complexity of Vector Addition Systems with States
Vector addition systems are an important model in theoretical computer science and have been used in a variety of areas. In this paper, we consider vector addition systems with states over a parameterized initial configuration. For these systems, we are interested in the standard notion of computati...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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2020
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7788602/ http://dx.doi.org/10.1007/978-3-030-45231-5_32 |
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author | Zuleger, Florian |
author_facet | Zuleger, Florian |
author_sort | Zuleger, Florian |
collection | PubMed |
description | Vector addition systems are an important model in theoretical computer science and have been used in a variety of areas. In this paper, we consider vector addition systems with states over a parameterized initial configuration. For these systems, we are interested in the standard notion of computational time complexity, i.e., we want to understand the length of the longest trace for a fixed vector addition system with states depending on the size of the initial configuration. We show that the asymptotic complexity of a given vector addition system with states is either [Formula: see text] for some computable integer k, where N is the size of the initial configuration, or at least exponential. We further show that k can be computed in polynomial time in the size of the considered vector addition system. Finally, we show that [Formula: see text] , where n is the dimension of the considered vector addition system. |
format | Online Article Text |
id | pubmed-7788602 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
record_format | MEDLINE/PubMed |
spelling | pubmed-77886022021-01-07 The Polynomial Complexity of Vector Addition Systems with States Zuleger, Florian Foundations of Software Science and Computation Structures Article Vector addition systems are an important model in theoretical computer science and have been used in a variety of areas. In this paper, we consider vector addition systems with states over a parameterized initial configuration. For these systems, we are interested in the standard notion of computational time complexity, i.e., we want to understand the length of the longest trace for a fixed vector addition system with states depending on the size of the initial configuration. We show that the asymptotic complexity of a given vector addition system with states is either [Formula: see text] for some computable integer k, where N is the size of the initial configuration, or at least exponential. We further show that k can be computed in polynomial time in the size of the considered vector addition system. Finally, we show that [Formula: see text] , where n is the dimension of the considered vector addition system. 2020-04-17 /pmc/articles/PMC7788602/ http://dx.doi.org/10.1007/978-3-030-45231-5_32 Text en © The Author(s) 2020 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 Zuleger, Florian The Polynomial Complexity of Vector Addition Systems with States |
title | The Polynomial Complexity of Vector Addition Systems with States |
title_full | The Polynomial Complexity of Vector Addition Systems with States |
title_fullStr | The Polynomial Complexity of Vector Addition Systems with States |
title_full_unstemmed | The Polynomial Complexity of Vector Addition Systems with States |
title_short | The Polynomial Complexity of Vector Addition Systems with States |
title_sort | polynomial complexity of vector addition systems with states |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7788602/ http://dx.doi.org/10.1007/978-3-030-45231-5_32 |
work_keys_str_mv | AT zulegerflorian thepolynomialcomplexityofvectoradditionsystemswithstates AT zulegerflorian polynomialcomplexityofvectoradditionsystemswithstates |