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. This problem was shown to be undecidable some ten years ago for WTGs making use of at least three clocks, and is known to be decidable for single-clock WTGs. In this paper, we establish undecidability for two-clock WTGs making use of non-negative weights, even in a time-bounded setting, closing one of the last remaining major gaps in our algorithmic understanding of WTGs.
Submitted, 2025. 23 pages.
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© 2025 Quentin Guilmant, Joël
Ouaknine, and Isa Vialard.