Multi-weighted Reachability Games

Brihaye, Thomas; Goeminne, Aline

doi:10.1007/978-3-031-45286-4_7

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Multi-weighted Reachability Games

Brihaye, Thomas; Goeminne, Aline

2023 • In Bournez, Olivier (Ed.) Reachability Problems - 17th International Conference, RP 2023, Proceedings

Peer reviewed

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https://hdl.handle.net/20.500.12907/47728

DOI
10.1007/978-3-031-45286-4_7

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Keywords :

lexico-optimal strategies; Pareto-optimal strategies; two-player games on graphs; Reachability; multi-weighted reachability games

Abstract :

[en] We study two-player multi-weighted reachability games played on a finite directed graph, where an agent, called P1, has several quantitative reachability objectives that he wants to optimize against an antagonistic environment, called P2. In this setting, we ask what cost profiles P1 can ensure regardless of the opponent’s behavior. Cost profiles are compared thanks to: (i) a lexicographic order that ensures the unicity of an upper value and (ii) a componentwise order for which we consider the Pareto frontier. We synthesize (i) lexico-optimal strategies and (ii) Pareto-optimal strategies. The strategies are obtained thanks to a fixpoint algorithm which also computes the upper value in polynomial time and the Pareto frontier in exponential time. Finally, the constrained existence problem is proved in PTIME for the lexicographic order and PSPACE -complete for the componentwise order.

Disciplines :

Computer science

Author, co-author :

Brihaye, Thomas ; Université de Mons - UMONS > Faculté des Science > Service de Mathématiques effectives

Goeminne, Aline ; Université de Mons - UMONS > Faculté des Science > Service de Mathématiques effectives

Language :

English

Title :

Multi-weighted Reachability Games

Publication date :

2023

Event name :

17th International Conference on Reachability Problems

Event place :

Nice, France

Event date :

11-10-2023 => 13-10-2023

Main work title :

Reachability Problems - 17th International Conference, RP 2023, Proceedings

Editor :

Bournez, Olivier

Publisher :

Springer Science and Business Media Deutschland GmbH

ISBN/EAN :

978-3-03-145285-7

Peer reviewed :

Peer reviewed

Additional URL :

https://link.springer.com/content/pdf/10.1007/978-3-031-45286-4_7

Research unit :

S820 - Mathématiques effectives

Research institute :

R150 - Institut de Recherche sur les Systèmes Complexes

Name of the research project :

5581 - CR-Brihaye - RobSynthMulTiGa - Fédération Wallonie Bruxelles
5330 - PDR-Brihaye - RatBeCoSi - Fédération Wallonie Bruxelles

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique

Funding text :

T. Brihaye—Partly supported by the F.R.S.-FNRS under grant n◦T.0027.21. A. Goeminne— Postdoctoral Researcher of the Fonds de la Recherche Scientifique - FNRS.

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