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Inaproximability in Weighted Timed Games

Authors Quentin Guilmant , Joël Ouaknine

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Author Details

Quentin Guilmant
  • Max Planck Institute for Software Systems, Saarland Informatics Campus, Saarbrücken, Germany
Joël Ouaknine
  • Max Planck Institute for Software Systems, Saarland Informatics Campus, Saarbrücken, Germany

Funding

  • Ouaknine, Joël: Also affiliated with Keble College, Oxford as https://emmy.network/ Fellow, and supported by DFG grant 389792660 as part of https://perspicuous-computing.science.

Cite AsGet BibTex

Quentin Guilmant and Joël Ouaknine. Inaproximability in Weighted Timed Games. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 27:1-27:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CONCUR.2024.27

Abstract

We consider two-player, turn-based weighted timed games played on timed automata equipped with (positive and negative) integer weights, in which one player seeks to reach a goal location whilst minimising the cumulative weight of the underlying path. Although the value problem for such games (is the value of the game below a given threshold?) is known to be undecidable, the question of whether one can approximate this value has remained a longstanding open problem. In this paper, we resolve this question by showing that approximating arbitrarily closely the value of a given weighted timed game is computationally unsolvable.

Subject Classification

ACM Subject Classification
  • Theory of computation → Program verification
Keywords
  • Weighted timed games
  • approximation
  • undecidability

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