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Minkowski Games

Stéphane Le Roux, Arno Pauly Orcid Logo, Jean-François Raskin

ACM Transactions on Computational Logic, Volume: 19, Issue: 3, Pages: 1 - 29

Swansea University Author: Arno Pauly Orcid Logo

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DOI (Published version): 10.1145/3230741

Abstract

We introduce and study Minkowski games. These are two player games, where the players take turns to choose positions in R^d based on some rules. Variants include boundedness games, where one player wants to keep the positions bounded, and the other wants to escape to infinity; as well as safety game...

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Published in: ACM Transactions on Computational Logic
ISSN: 1529-3785 1557-945X
Published: Association for Computing Machinery (ACM) 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa40809
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first_indexed 2018-06-26T12:03:22Z
last_indexed 2023-01-11T14:17:26Z
id cronfa40809
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spelling 2022-12-05T12:47:36.8161185 v2 40809 2018-06-25 Minkowski Games 17a56a78ec04e7fc47b7fe18394d7245 0000-0002-0173-3295 Arno Pauly Arno Pauly true false 2018-06-25 SCS We introduce and study Minkowski games. These are two player games, where the players take turns to choose positions in R^d based on some rules. Variants include boundedness games, where one player wants to keep the positions bounded, and the other wants to escape to infinity; as well as safety games, where one player wants to stay within a prescribed set, while the other wants to leave it.We provide some general characterizations of which player can win such games, and explore the computational complexity of the associated decision problems. A natural representation of boundedness games yields coNP-completeness, whereas the safety games are undecidable. Journal Article ACM Transactions on Computational Logic 19 3 1 29 Association for Computing Machinery (ACM) 1529-3785 1557-945X game theory; verification of hybrid systems; polytopes 18 9 2018 2018-09-18 10.1145/3230741 COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2022-12-05T12:47:36.8161185 2018-06-25T13:48:55.7611145 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Stéphane Le Roux 1 Arno Pauly 0000-0002-0173-3295 2 Jean-François Raskin 3 0040809-25062018135152.pdf 1609.07048.pdf 2018-06-25T13:51:52.3700000 Output 341203 application/pdf Accepted Manuscript true 2018-06-25T00:00:00.0000000 true eng
title Minkowski Games
spellingShingle Minkowski Games
Arno Pauly
title_short Minkowski Games
title_full Minkowski Games
title_fullStr Minkowski Games
title_full_unstemmed Minkowski Games
title_sort Minkowski Games
author_id_str_mv 17a56a78ec04e7fc47b7fe18394d7245
author_id_fullname_str_mv 17a56a78ec04e7fc47b7fe18394d7245_***_Arno Pauly
author Arno Pauly
author2 Stéphane Le Roux
Arno Pauly
Jean-François Raskin
format Journal article
container_title ACM Transactions on Computational Logic
container_volume 19
container_issue 3
container_start_page 1
publishDate 2018
institution Swansea University
issn 1529-3785
1557-945X
doi_str_mv 10.1145/3230741
publisher Association for Computing Machinery (ACM)
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
document_store_str 1
active_str 0
description We introduce and study Minkowski games. These are two player games, where the players take turns to choose positions in R^d based on some rules. Variants include boundedness games, where one player wants to keep the positions bounded, and the other wants to escape to infinity; as well as safety games, where one player wants to stay within a prescribed set, while the other wants to leave it.We provide some general characterizations of which player can win such games, and explore the computational complexity of the associated decision problems. A natural representation of boundedness games yields coNP-completeness, whereas the safety games are undecidable.
published_date 2018-09-18T03:51:58Z
_version_ 1763752561136893952
score 11.013148

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