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

对于知识用户和科学家来说，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(与连续动力系统形成对比，在连续动力系统中，微积分、线性代数、叠加原理和发展良好的工程计算工具是可用的，并在过去几个世纪得到发展)。有限离散事件动态系统模型在自然科学和工程中普遍存在：有限离散事件动态系统模型在整个自然科学和工程中无处不在：常见的建模技术包括有限自动机、PETRI网、生物和化学中的反应网络、基因调控网络、布尔和多值逻辑网络、皮质柱状神经模型、图-从理论上描述具有不同转换类型和时间尺度的系统，以及动态网络(其状态空间可以自适应地增长或缩小，同时保持有限)。所有这些都是随着外部事件和内部转变而变化的日益流行的计算模型。*这项研究将创建21世纪的计算工具，这些工具植根于19世纪和20世纪的严格定理，这些定理来自数学对称理论和自动机的代数理论，这些定理确保始终可以为给定的有限(通常是无限)离散事件动力系统创建一个全局的、分层组织的坐标系。这些计算坐标系将允许一个人‘导航’给定的离散事件系统，知道系统状态的‘纬度和经度’，以及如何通过一系列步骤将其转换到另一个所需的状态。一种特殊情况是小数展开对算术的影响：人们可以在位置记数法中进行计算，遵循与沿位置层次的值的变化相关联的高度受限的进位法则，其中值的变化以简单的方式计算，例如逐个添加一位数。以从粗到精的方式对全局系统状态的这种抽象表示是可能的(不仅对于数字)，而且对于任何有限的离散事件系统，并且可以促进样本应用中的简单操作，例如如何：*-让AI自动集成不同的信息以推荐策略和离散的动作以实现期望的目标*-在战略形势/战术游戏中，以紧凑的信息形式简明地表示游戏状态，以供人类操作员有效地移动到期望的配置*-通过系统地‘调整’其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.