发表机构
The Pennsylvania State University（宾夕法尼亚州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文精炼可计算分析方法，研究贝尔曼优化问题，证明每个实例存在任意小均匀可计算扰动使最短路径长度可计算，最优路径类为 $\Pi_1^0$ 类。
AI 中文摘要
本文的目标是精炼可计算分析中的方法，并将其用于研究贝尔曼提出的一个优化问题的解。该问题询问如何找到不适合给定平面图形的最优（最短）路径。我们证明，贝尔曼问题的每个实例都有一个任意小的均匀可计算扰动，对于该扰动，路径的最小长度是可计算的，因此最优路径类是一个 $\Pi_1^0$ 类，并且存在均匀可计算的路径，其长度任意小地大于最小可能值。
英文摘要
The goal of this paper is to refine methods in computable analysis and to employ them in the study of solutions of an optimization problem posed by Bellman. This problem asks how to find optimal (shortest) paths which do not fit into given plane figures. We show that each instance of Bellman's problem has an arbitrarily small uniformly computable perturbation for which the minimal length of path is computable, and thus the class of optimal paths is a $Π_1^0$ class, and there are uniformly computable paths which escape with arbitrarily small length greater than the minimum possible.
Comments22 pages, 0 figures
