一阶结构上的抽象计算：附加内容：从程序到决策树 I
Abstract computation over first-order structures. Extras: From programs to decision trees I
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中文总结 AI 辅助
本文提出关联一阶结构相关模型的理论框架，引入程序路径与迁移系统，定义其标准序并给出有限程序路径的枚举算法，为分析BSS机器等的决策提供支撑。
中文摘要 AI 辅助
决策及其后果可通过决策树进行描述与分析，这些决策依赖于尽可能用“是”或“否”回答的问题。实数上的原始BSS机器是带有计算节点和决策分支节点的图；计算机辅助几何中为各类数引入的BSS机器与代数决策树的求值，通常涉及一阶逻辑文字系统的求值。类流程图表示与决策树也有助于分析一阶结构上BSS RAM作出的决策，所有由BSS RAM面向机器的程序定义的算法，均可通过流程图、程序树中的游走及路径进行说明。这些工具的基本结构是图，其可视化表示有助于刻画单个BSS RAM及其他一阶机器的行为。本文提供了关联各类模型的理论框架，引入了用于转换部分配置的程序路径与迁移系统，这些配置是语法上定义的，后续可扩展与细化；最后定义了程序路径的标准序，并给出了有限程序路径的枚举算法。
英文摘要
Decisions and their consequences can be described and analyzed by means of decision trees. The decisions themselves depend on questions that, whenever possible, should be answered with yes or no. The original BSS machines over the real numbers are graphs with computation nodes and branching nodes for decisions. The evaluation of BSS machines and algebraic decision trees in computer-aided geometry which have been introduced for various types of numbers generally involves the evaluation of systems of literals of first-order logic. Flowchart-like representations and decision trees are also helpful for analyzing decisions made by BSS RAMs over first-order structures. All algorithms defined by machine-oriented programs of BSS RAMs can be illustrated using flowcharts, walks, and paths in program trees. The basic structures of these tools are graphs and their visual representations can help to characterize the behavior of individual BSS RAMs and other first-order machines. We offer a theoretical framework for linking various models. Here, we introduce program paths and transition systems for transforming partial configurations which are defined syntactically and can be extended and refined later. Finally, we define standard orders for program paths and present algorithms for enumerating finite program paths.
