Toward an Algebraic Theory of Systems

Understand

We propose the concept of a system algebra with a parallel composition operation and an interface connection operation, and formalize composition-order invariance, which postulates that the order of composing and connecting systems is irrelevant, a generalized form of associativity.

• Composition-order invariance explicitly captures a common property that is implicit in any context where one can draw a figure (hiding the drawing order) of several connected systems, which appears in many scientific contexts.
• This abstract algebra captures settings where one is interested in the behavior of a composed system in an environment and wants to abstract away anything internal not relevant for the behavior.
• This may include physical systems, electronic circuits, or interacting distributed systems.