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The Control of Synchronous Systems, Part Ⅱ

机译:同步系统的控制,第二部分

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摘要

A controller is an environment for a system that achieves a particular control objective by providing inputs to the system without constraining the choices of the system. For synchronous systems, where system and controller make simultaneous and interdependent choices, the notion that a controller must not constrain the choices of the system can be formalized by type systems for composability. In a previous paper, we solved the control problem for static and dynamic types: a static type is a dependency relation between inputs and outputs, and composition is well-typed if it does not introduce cyclic dependencies; a dynamic type is a set of static types, one for each state. Static and dynamic types, however, cannot capture many important digital circuits, such as gated clocks, bidirectional buses, and random-access memory. We therefore introduce more general type systems, so-called dependent and bidirectional types, for modeling these situations, and we solve the corresponding control problems. In a system with a dependent type, the dependencies between inputs and outputs are determined gradually through a game of the system against the controller. In a system with a bidirectional type, also the distinction between inputs and outputs is resolved dynamically by such a game. The game proceeds in several rounds. In each round the system and the controller choose to update some variables dependent on variables that have already been updated. The solution of the control problem for dependent and bidirectional types is based on algorithms for solving these games.
机译:控制器是一种系统环境,它通过在不限制系统选择的情况下向系统提供输入来实现特定的控制目标。对于同步系统,其中系统和控制器做出同时且相互依赖的选择,对于类型的可组合性,可以用类型系统形式化控制器不能限制系统选择的概念。在先前的论文中,我们解决了静态和动态类型的控制问题:静态类型是输入和输出之间的依赖关系,如果不引入循环依赖关系,则组合类型是正确的;动态类型是一组静态类型,每个状态一个。但是,静态和动态类型无法捕获许多重要的数字电路,例如门控时钟,双向总线和随机存取存储器。因此,我们引入了更通用的类型系统,即所谓的从属类型和双向类型,以对这些情况进行建模,并解决了相应的控制问题。在具有依赖类型的系统中,输入和输出之间的依赖关系是通过系统与控制器的博弈逐渐确定的。在具有双向类型的系统中,输入和输出之间的区别也可以通过这种游戏动态地解决。游戏进行了几轮。在每个回合中,系统和控制器都会根据已更新的变量选择更新一些变量。依赖类型和双向类型的控制问题的解决方案基于解决这些博弈的算法。

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