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arXiv · 2508.00014

Deciding the Value of Two-Clock Almost Non-Zeno Weighted Timed Games

Isa Vialard
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Abstract

The Value Problem for weighted timed games (wtgs) consists in determining, given a two-player weighted timed game with a reachability objective and a rational threshold, whether or not the value of the game exceeds the threshold. When restrained to wtgs with non-negative weight, this problem is known to be undecidable for weighted timed games with three or more clocks, and decidable for one-clock wtgs. The Value Problem for two-clock non-negative wtgs, which remained stubbornly open for a decade, was recently shown to be undecidable. In this article, we show that the Value Problem is decidable when considering two-clock almost non-Zeno wtgs.

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Isa Vialard. 2025-07-24. Deciding the Value of Two-Clock Almost Non-Zeno Weighted Timed Games. https://arxiv.org/abs/2508.00014

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