Abstract
Communicating Concurrent Kleene Algebra (C²KA) is a mathematical
framework for capturing the communicating and concurrent behaviour of
agents in distributed systems. It extends Hoare et al.'s
Concurrent Kleene Algebra (CKA) with communication actions through the
notions of stimuli and shared environments. C²KA has applications in
studying system-level properties of distributed systems such as
safety, security, and reliability. In this work, we formalize results
about C²KA and its application for distributed systems specification.
We first formalize the stimulus structure and behaviour structure
(CKA). Next, we combine them to formalize C²KA and its properties.
Then, we formalize notions and properties related to the topology of
distributed systems and the potential for communication via stimuli
and via shared environments of agents, all within the algebraic
setting of C²KA.