A method for specifying the behavior and architecture of discrete state systems such as digital electronic devices and software using deterministic state machines and automata products. The state machines are represented by sequence maps $f:A^*\to X$ where $f(s)=x$ indicates that the output of the system is $x$ in the state reached by following the sequence of events $s$ from the initial state. Examples provided include counters, networks, reliable message delivery, real-time analysis of gates and latches, and producer/consumer. Techniques for defining, parameterizing, characterizing abstract properties, and connecting sequence functions are developed. Sequence functions are shown to represent (possibly non-finite) Moore type state machines and general products of state machines. The method draws on state machine theory, automata products, and recursive functions and is ordinary working mathematics, not involving formal methods or any foundational or meta-mathematical techniques. Systems in which there are levels of components that may operate in parallel or concurrently are specified in terms of function composition.

中文翻译：

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大型计算机软件和系统的状态机

一种使用确定性状态机和自动机产品指定离散状态系统（例如数字电子设备和软件）的行为和体系结构的方法。状态机由序列映射 $f:A^*\to X$ 表示，其中 $f(s)=x$ 表示系统的输出为 $x$ 遵循事件序列 $s 所达到的状态$ 从初始状态。提供的示例包括计数器、网络、可靠的消息传递、门和锁存器的实时分析以及生产者/消费者。开发了用于定义、参数化、表征抽象属性和连接序列函数的技术。序列函数表示（可能是非有限的）摩尔型状态机和状态机的一般乘积。该方法借鉴了状态机理论、自动机产品、和递归函数，是普通的工作数学，不涉及形式方法或任何基础或元数学技术。在功能组合方面指定了可以并行或并发运行的组件级别的系统。