点火同步问题的最新解及其下界
An Overview of Recent Solutions to and Lower Bounds for the Firing Synchronization Problem
摘要：
在生物建模、图像处理和语言识别等广泛领域的复杂系统可以使用称为有限自动机的非常简单的机器网络来建模。将使用有限自动机建模的子系统连接到一个网络中可以提供更多的计算能力。一个这样的网络，称为细胞自动机，由一个n维数组（n > 1）和一个位于数组每一点的有限自动机组成。与细胞自动机相关的最古老的问题之一是点火同步问题，最初由John Myhill在1957年提出。与任何长期存在的问题一样，有大量的解决方案来解决点火同步问题。我们的目标以及这项工作的贡献是总结该问题的最新解决方案。我们主要关注原始问题的解决方案，即网络是一维数组并且在一端有一个单一发起者的问题。我们总结了最小时间和非最小时间的解决方案，重点是1998年以后发表的解决方案。我们还专注于解决方案，最大限度地减少有限自动机所需的状态数。在这个过程中，我们还确定了开放的问题，仍然在寻找最小状态的解决方案的点火同步问题。
英文摘要：
Complex systems in a wide variety of areas such as biological modeling, image processing, and language recognition can be modeled using networks of very simple machines called finite automata. Connecting subsystems modeled using finite automata into a network allows for more computational power. One such network, called a cellular automaton, consists of an n-dimensional array for n > 1 with a single finite automaton located at each point of the array. One of the oldest problems associated with cellular automata is the firing synchronization problem, originally proposed by John Myhill in 1957. As with any long-standing problem, there are a large number of solutions to the firing synchronization problem. Our goal, and the contribution of this work, is to summarize recent solutions to the problem. We focus primarily on solutions to the original problem, that is, the problem where the network is a one-dimensional array and there is a single initiator located at one of the ends. We summarize both minimal-time and non-minimal-time solutions, with an emphasis on solutions that were published after 1998. We also focus on solutions that minimize the number of states required by the finite automata. In the process we also identify open problems that remain in terms of finding minimal-state solutions to the firing synchronization problem.
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