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Documents authored by Guilmant, Quentin


Document
Inaproximability in Weighted Timed Games

Authors: Quentin Guilmant and Joël Ouaknine

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)


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.

Cite as

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)


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@InProceedings{guilmant_et_al:LIPIcs.CONCUR.2024.27,
  author =	{Guilmant, Quentin and Ouaknine, Jo\"{e}l},
  title =	{{Inaproximability in Weighted Timed Games}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{27:1--27:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.27},
  URN =		{urn:nbn:de:0030-drops-207998},
  doi =		{10.4230/LIPIcs.CONCUR.2024.27},
  annote =	{Keywords: Weighted timed games, approximation, undecidability}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
The 2-Dimensional Constraint Loop Problem Is Decidable

Authors: Quentin Guilmant, Engel Lefaucheux, Joël Ouaknine, and James Worrell

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)


Abstract
A linear constraint loop is specified by a system of linear inequalities that define the relation between the values of the program variables before and after a single execution of the loop body. In this paper we consider the problem of determining whether such a loop terminates, i.e., whether all maximal executions are finite, regardless of how the loop is initialised and how the non-determinism in the loop body is resolved. We focus on the variant of the termination problem in which the loop variables range over ℝ. Our main result is that the termination problem is decidable over the reals in dimension 2. A more abstract formulation of our main result is that it is decidable whether a binary relation on ℝ² that is given as a conjunction of linear constraints is well-founded.

Cite as

Quentin Guilmant, Engel Lefaucheux, Joël Ouaknine, and James Worrell. The 2-Dimensional Constraint Loop Problem Is Decidable. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 140:1-140:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{guilmant_et_al:LIPIcs.ICALP.2024.140,
  author =	{Guilmant, Quentin and Lefaucheux, Engel and Ouaknine, Jo\"{e}l and Worrell, James},
  title =	{{The 2-Dimensional Constraint Loop Problem Is Decidable}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{140:1--140:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.140},
  URN =		{urn:nbn:de:0030-drops-202831},
  doi =		{10.4230/LIPIcs.ICALP.2024.140},
  annote =	{Keywords: Linear Constraints Loops, Minkowski-Weyl, Convex Sets, Asymptotic Expansions}
}
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