Compositional Cyber-Physical Systems Theory
This addresses the challenge of formal assurance for complex cyber-physical systems, though it appears incremental as it builds on existing horizontal composition methods.
The dissertation tackles the problem of ensuring safety and security in cyber-physical systems by developing a compositional theory that relates requirements, behaviors, and architectures, using category theory to enable verified vertical composition across these models.
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.