Rough analysis of computation trees

TL;DR

This paper analyzes the relationships between problem description complexity and the minimum complexity of deterministic and nondeterministic computation trees over arbitrary structures, classifying possible relation types and their growth with input size.

Contribution

It provides a rough classification of all possible relation types among these parameters and studies how these relations change as the number of input variables increases.

Findings

Enumerates all seven possible relation types among the parameters.

Studies the evolution of these relation types with increasing input variables.

Offers a framework for understanding the complexity relationships in computation trees.

Abstract

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.