A Mathematical Framework and Theory Governing the Verification of Autonomous Systems

Abstract

Autonomous systems are varied, complex, and designed to accomplish dynamic goals. Consequently, the problem of verifying autonomous systems is difficult to stage and solve when only the performance of a system’s components is known. We define a mathematical framework that relies on category theory to represent capabilities in a way that allows us to usefully combine them into a measure of system performance. We allow for black box capabilities with vaguely defined performance metrics, and define a capability graph which can connect capabilities in an arbitrary structure. Our proposed framework has the flexibility to accommodate behavior patterns and goals for a large variety of current and future systems across disciplines. We discuss the framework, the mechanisms which can be used to verify autonomous systems and how sheaf theory can be utilized to estimate system performance. Notably, we apply key theorems of the framework to identify capability gaps, as well as discuss additional applications of the framework.