计算树的粗略分析

摘要：

本文讨论了任意结构上的计算树，该结构由一个集合以及定义在该集合上的函数和谓词的集合组成，并致力于比较分析在这种结构上具有$n$输入变量的问题的三个参数：问题描述的复杂性，确定性地解决该问题的计算树的最小复杂性，以及非确定性地解决该问题的计算树的最小复杂性。粗略分类这些参数之间的关系被认为是所有可能的七种类型的这些关系被枚举。研究了关系类型随输入变量个数$n$的变化。

英文摘要：

This paper deals with computation trees over an arbitrary structure consisting of a set along with collections of functions and predicates that are defined on it. It is devoted to the comparative analysis of three parameters of problems with $n$ input variables over this structure: the complexity of a problem description, the minimum complexity of a computation tree solving this problem deterministically, and the minimum complexity of a computation tree solving this problem nondeterministically. Rough classification of relationships among these parameters is considered and all possible seven types of these relations are enumerated. The changes of relation types with the growth of the number $n$ of input variables are studied.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。