Viable Algorithmic Options for Creating and Adapting Emergent Software Systems

TL;DR

This paper analyzes the computational complexity of creating and adapting emergent software systems, showing intractability in general and under restrictions, but also identifying conditions that lead to tractability.

Contribution

It provides a complexity analysis of algorithms for self-adapting software systems and identifies restrictions that make these problems computationally feasible.

Findings

Neither creation nor adaptation is solvable for all inputs without restrictions.

Restrictions on system structure can lead to tractability.

Adaptation is computationally easier than creation under certain conditions.

Abstract

Given the complexity of modern software systems, it is of great importance that such systems be able to autonomously modify themselves, i.e., self-adapt, with minimal human supervision. It is critical that this adaptation both results in reliable systems and scales reasonably in required memory and runtime to non-trivial systems. In this paper, we apply computational complexity analysis to evaluate algorithmic options for the reliable creation and adaptation of emergent software systems relative to several popular types of exact and approximate efficient solvability. We show that neither problem is solvable for all inputs when no restrictions are placed on software system structure. This intractability continues to hold relative to all examined types of efficient exact and approximate solvability when software systems are restricted to run (and hence can be verified against system requirements) in polynomial time. Moreover, both of our problems when so restricted remain intractable under a variety of additional restrictions on software system structure, both individually and in many combinations. That being said, we also give sets of additional restrictions that do yield tractability for both problems, as well as circumstantial evidence that emergent software system adaptation is computationally easier than emergent software system creation.