The synthesis of controllers for reactive systems can be done by computing winning strategies in two-player games. Timed (game) Automata are an appropriate formalism to model real-time embedded systems but are not easy to use for controller synthesis for two reasons: i) timed models require the knowledge of the precise timings of the system; for example, if an action must occur in the future, the deadline of this occurrence must be known, ii) in practice, the dense state space makes the computation of the controller often impossible for complex systems. This paper introduces an extension of untimed game automata with logical time. The new semantics introduces two new types of uncontrollable actions: delayed actions which are possibly avoidable, and ineluctable actions which will eventually happen if nothing is done to abort it. The controller synthesis problem is adapted to this new semantics. This paper focuses specifically on the reachability and safety objectives and gives algorithms to generate a controller. The paper then extends these results to Game Petri Nets which can express concurrent timed behaviors and where an avoidable transition can lose its avoidability by the elapsing of time. The usefulness of this new model is illustrated by a real device driver synthesis example.

中文翻译：

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并发DES的逻辑时间控制

反应系统控制器的合成可以通过计算两人游戏中的获胜策略来完成。定时（游戏）自动机是对实时嵌入式系统建模的合适形式，但由于两个原因不易用于控制器综合：i) 定时模型需要了解系统的精确定时；例如，如果某个动作必须在未来发生，则必须知道该动作的截止日期，ii) 在实践中，稠密的状态空间使得复杂系统的控制器计算通常是不可能的。本文介绍了具有逻辑时间的不定时博弈自动机的扩展。新语义引入了两种新类型的不可控动作：可能可以避免的延迟动作，以及如果不采取任何措施中止它最终会发生的不可避免的动作。控制器综合问题适用于这种新的语义。本文特别关注可达性和安全性目标，并给出了生成控制器的算法。然后，论文将这些结果扩展到游戏 Petri 网，它可以表达并发的定时行为，并且可避免的转换会随着时间的流逝而失去其可避免性。一个真实的设备驱动程序综合示例说明了这种新模型的有用性。