Quantitative Games on Probabilistic Timed Automata

TL;DR

This paper extends the study of quantitative two-player zero-sum games from non-probabilistic to probabilistic timed automata, introducing quasi-simple functions to handle the probabilistic setting and analyzing the computational complexity of solving such games.

Contribution

It generalizes simple functions to quasi-simple functions for probabilistic timed automata and establishes the complexity class for solving these quantitative games.

Findings

Games with expected reachability-time are in NEXPTIME ∩ co-NEXPTIME.

Games with expected discounted-time are in NEXPTIME ∩ co-NEXPTIME.

Introduces quasi-simple functions to handle probabilistic aspects in timed automata.

Abstract

Two-player zero-sum games are a well-established model for synthesising controllers that optimise some performance criterion. In such games one player represents the controller, while the other describes the (adversarial) environment, and controller synthesis corresponds to computing the optimal strategies of the controller for a given criterion. Asarin and Maler initiated the study of quantitative games on (non-probabilistic) timed automata by synthesising controllers which optimise the time to reach a final state. The correctness and termination of their approach was dependent on exploiting the properties of a special class of functions, called simple functions, that can be finitely represented. In this paper we consider quantitative games over probabilistic timed automata. Since the concept of simple functions is not sufficient to solve games in this setting, we generalise simple functions to so-called quasi-simple functions. Then, using this class of functions, we demonstrate that the problem of solving games with either expected reachability-time or expected discounted-time criteria on probabilistic timed automata are in NEXPTIME $\cap$ co-NEXPTIME.