Automatic Computational Understanding and Manipulation of Finite Discrete-Event Dynamical Systems throughout Natural Sciences and Engineering

理解和预测操纵一类重要的模型，有限离散事件动力系统，仍然缺乏足够的预测框架的知识用户和科学家（与连续动力系统相比，微积分，线性代数，叠加原理和发达的工程计算工具是可用的，并已在过去几个世纪的发展）。深入理解有限离散事件动力系统的基础存在于其基本的数学基础中，但这需要通过一系列适用的方法，计算和数学工具来培养实践范式（1）在整个科学和工程中广泛利用，（2）增强人工智能和人类认知能力。有限离散事件动态系统模型在自然科学和工程中无处不在：常见的建模技术包括使用有限自动机、Petri网、生物学和化学中的反应网络、遗传调控网络、布尔和多值逻辑网络、皮质柱神经模型、具有不同过渡类型和时间尺度的图论描述系统，以及动态网络（其状态空间可以自适应地增长或收缩，同时保持有限）。所有这些都是越来越流行的计算模型，它们会随着外部事件和内部转变而发生变化。这项研究将创建21世纪世纪的计算工具植根于严格的19和20世纪世纪定理从对称性的数学理论和代数理论的自动机，保证它总是可以创建一个全球性的，分层组织的坐标系统为一个给定的有限（往往是无限的）离散事件动力系统。这些计算坐标系统将允许一个“导航”一个给定的离散事件系统，知道一个系统状态的“纬度和经度”，以及如何通过一系列步骤将其转换为另一个所需的状态。一个特殊的情况是十进制展开式对算术的作用：人们可以用位置记法进行计算，遵循高度限制的"进位定律"，该定律将值的变化沿着位置的层次关系，其中值的变化以简单的方式计算，例如逐个添加个位数。这样一种从粗到细的全局系统状态的抽象表示是可能的（不仅仅是数字），而且适用于任何有限离散事件系统，并且可以在示例应用程序中方便操作，例如如何：- 让AI自动整合各种信息，以推荐策略和离散动作，以实现预期目标-在战略情况/战术游戏中，以紧凑信息形式简明地表示人类操作者有效地移动到期望配置的游戏状态-通过系统地“调整”癌细胞的状态坐标来操纵癌细胞以诱导其接近非恶性状态。

Understanding and predictively manipulating an important class of models, finitary discrete-event dynamical systems, still lacks adequate predictive frameworks for knowledge users and scientists (in contrast to continuous dynamical systems where calculus, linear algebra, superposition principles and well-developed engineering computational tools are available and have been developed over the last several centuries). Groundwork for deep understanding of finite discrete-event dynamical systems exists in its basic mathematical underpinnings, but this needs to be nurtured into a paradigm of practice with an applicable body of methodological, computational and mathematical tools (1) to be widely exploited throughout Science and Engineering, and (2) to augment AI and human cognitive capabilities. Finite discrete-event dynamical systems models are ubiquitous throughout natural science and engineering: Common modelling techniques include the use of finite automata, Petri nets, reaction networks in biology and chemistry, genetic regulatory networks, Boolean and multivalued logic networks, cortical column neural models, graph-theoretically described systems with different transition types and time-scales, and dynamic networks (whose state-spaces may grow or shrink adaptively, while remaining finite). All are increasingly prevalent computational models that transform in response to external events and internal transitions. This research will create 21st century computational tools rooted in rigorous 19th and 20th century theorems from the mathematical theory of symmetry and algebraic theory of automata that guarantee it is always possible to create a global, hierarchically organized system of coordinates for a given finite (and often infinite) discrete-event dynamical system. These computational coordinate systems will allow one to 'navigate' a given discrete event system, to know the 'latitude and longitude' of a system state, and how to transform it by a sequence of steps into another desired state. A special case is what the decimal expansion does for arithmetic: one can calculate in a positional notation, following highly restricted 'carry laws' that relate change in values along the hierarchy of positions, where change of value is computed in a simple way, e.g. adding single digits, one-by-one. Such an abstract representation of global system state in a coarse-to-fine manner is possible (not just for numbers), but for any finite discrete-event system, and could facilitate easy manipulation in sample applications such as how to: -let AI automatically integrate diverse information to recommend strategies and discrete moves to achieve a desired goal -in a strategic situation / tactical game, concisely represent state of play in compact informative form for a human operator to move effectively to a desired configuration -manipulate a cancerous cell to induce it to approach to a non-malignant state by systematically 'adjusting' its state coordinates.