Decidability of One-Clock Weighted Timed Games with Arbitrary Weights

Weighted Timed Games (WTG for short) are the most widely used model to describe controller synthesis problems involving real-time issues. Unfortunately, they are notoriously difficult, and undecidable in general. As a consequence, one-clock WTGs have attracted a lot of attention, especially because...

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Bibliographic Details
Published in:	Logical methods in computer science Vol. 21, Issue 1
Main Authors:	Monmege, Benjamin, Parreaux, Julie, Reynier, Pierre-Alain
Format:	Journal Article
Language:	English
Published:	Logical Methods in Computer Science Association 01.01.2025 Logical Methods in Computer Science e.V
Subjects:	Computation and Language Computer Science computer science - computer science and game theory Computer Science and Game Theory Formal Languages and Automata Theory Logic in Computer Science algorithmic game theory timed automata value computation weighted timed games
ISSN:	1860-5974, 1860-5974
Online Access:	Get full text
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Summary:	Weighted Timed Games (WTG for short) are the most widely used model to describe controller synthesis problems involving real-time issues. Unfortunately, they are notoriously difficult, and undecidable in general. As a consequence, one-clock WTGs have attracted a lot of attention, especially because they are known to be decidable when only non-negative weights are allowed. However, when arbitrary weights are considered, despite several recent works, their decidability status was still unknown. In this paper, we solve this problem positively and show that the value function can be computed in exponential time (if weights are encoded in unary).
ISSN:	1860-5974 1860-5974
DOI:	10.46298/lmcs-21(1:8)2025