Signal machines form an abstract and idealised model of collision computing. Based on dimensionless signals moving on the real line, they model particle/signal dynamics in Cellular Automata. Each particle, or signal, moves at constant speed in continuous time and space. When signals meet, they get replaced by other signals. A signal machine defines the types of available signals, their speeds and the rules for replacement in collision. A signal machine A simulates another one B if all the space-time diagrams of B can be generated from space-time diagrams of A by removing some signals and renaming other signals according to local information. Given any finite set of speeds S, we construct a signal machine that is able to simulate any signal machine whose speeds belong to S. Each signal is simulated by a macro-signal, a ray of parallel signals. Each macro-signal has a main signal located exactly where the simulated signal would be, as well as auxiliary signals which encode its id and the collision rules of the simulated machine. The simulation of a collision, a macro-collision, consists of two phases. In the first phase, macro-signals are shrunk, then the macro-signals involved in the collision are identified and it is ensured that no other macro-signal comes too close. If some do, the process is aborted and the macro-signals are shrunk, so that the correct macro-collision will eventually be restarted and successfully initiated. Otherwise, the second phase starts: the appropriate collision rule is found and new macro-signals are generated accordingly. Considering all finite set of speeds S and their corresponding simulators provides an intrinsically universal family of signal machines.
翻译:信号机器形成一个抽象和理想的碰撞计算模型。 基于在真实线上移动的无空间信号, 它们模拟在 Cellulal Automata 中的粒子/ 信号动态。 每个粒子或信号在连续的时间和空间中以恒定速度移动。 当信号相交时, 它们会被其他信号所取代。 信号机器定义了可用信号的类型、 其速度和在碰撞中替换的规则。 一个信号机器 A 模拟另一个 B, 如果B 的全部空间时间图能够从 A 的空时图中生成, 通过删除某些信号并根据当地信息重新命名其他信号。 鉴于任何数量有限的速度 S, 我们建立一个能够模拟任何信号机器的粒子/ 信号在连续的时间和空隙中以恒定速度移动。 每个信号都由宏观信号模拟, 每个宏观信号的主要信号都位于模拟信号的准确位置, 以及用来编码其身份和模拟机器的碰撞规则的辅助信号将会被成功找到。 碰撞的模拟、 宏观- 由两个阶段构成两个阶段的宏观- 。 在第一个阶段里, 开始的宏观标志会开始, 开始的宏观规则会自动 开始, 开始, 开始, 开始的宏观 开始, 开始的宏观 开始 开始 开始 开始 开始 开始 开始 和 开始的宏观 开始的 开始的 开始的宏观 的 开始 开始的 开始的 开始的 开始的 开始 的 的 的 的 开始的 的 的 。