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.
@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} }
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