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Abstract: Two-player zero-sum games are a well-established model for synthesisingcontrollers that optimise some performance criterion. In such games one playerrepresents the controller, while the other describes the adversarialenvironment, and controller synthesis corresponds to computing the optimalstrategies of the controller for a given criterion. Asarin and Maler initiatedthe study of quantitative games on non-probabilistic timed automata bysynthesising controllers which optimise the time to reach a final state. Thecorrectness and termination of their approach was dependent on exploiting theproperties of a special class of functions, called simple functions, that canbe finitely represented. In this paper we consider quantitative games overprobabilistic timed automata. Since the concept of simple functions is notsufficient to solve games in this setting, we generalise simple functions toso-called quasi-simple functions. Then, using this class of functions, wedemonstrate that the problem of solving games with either expectedreachability-time or expected discounted-time criteria on probabilistic timedautomata are in NEXPTIME $\cap$ co-NEXPTIME.



Author: Marta Kwiatkowska, Gethin Norman, Ashutosh Trivedi

Source: https://arxiv.org/



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