Compositional Cyber-Physical Systems Theory

TL;DR

This dissertation develops a compositional theory for cyber-physical systems using category theory to enable formal vertical composition across requirements, behaviors, and architectures for improved safety and security assurance.

Contribution

It introduces a novel vertical composition framework for cyber-physical systems using category theory, unifying diverse models and formalizing their relationships.

Findings

Category theory effectively relates different system models.

Vertical composition enhances system safety and security.

Formal semantics improve system verification processes.

Abstract

This dissertation builds a compositional cyber-physical systems theory to develop concrete semantics relating the above diverse views necessary for safety and security assurance. In this sense, composition can take two forms. The first is composing larger models from smaller ones within each individual formalism of requirements, behaviors, and architectures which can be thought of as horizontal composition -- a problem which is largely solved. The second and main contribution of this theory is vertical composition, meaning relating or otherwise providing verified composition across requirement, behavioral, and architecture models and their associated algebras. In this dissertation, we show that one possible solution to vertical composition is to use tools from category theory. Category theory is a natural candidate for making both horizontal and vertical composition formally explicit because it can relate, compare, and/or unify different algebras.