Resource Bounded Immunity and Simplicity

TL;DR

This paper explores various resource-bounded immunity and simplicity notions, analyzing their structural properties and proposing the k-immune hypothesis as a means to ensure simple sets exist within NP.

Contribution

It provides a comprehensive structural analysis of immunity and simplicity notions and introduces the k-immune hypothesis for NP complexity class.

Findings

Structural characteristics of immunity and simplicity notions analyzed.

Introduction of the k-immune hypothesis for NP.

Insights into the existence of simple sets in NP.

Abstract

Revisiting the thirty years-old notions of resource-bounded immunity and simplicity, we investigate the structural characteristics of various immunity notions: strong immunity, almost immunity, and hyperimmunity as well as their corresponding simplicity notions. We also study limited immunity and simplicity, called k-immunity and feasible k-immunity, and their simplicity notions. Finally, we propose the k-immune hypothesis as a working hypothesis that guarantees the existence of simple sets in NP.