A process algebra for the Span(Graph) model of concurrency

In this note we define a process algebra TCP (Truly Concurrent Processes) which corresponds closely with the automata model of concurrency based on Span(RGraph), the category of spans of reflexive graphs. In TCP, each process has a fixed set of interfaces. Actions are allowed to occur simultaneously on all the interfaces of a process. Asynchrony is modelled by the use of silent actions. Communication is anonymous: communication between two processes P and Q is described by an operation which connects some of the ports of P to some of the ports of Q; and a process can only communicate with other processes via its interfaces. The model is naturally equipped with a compositional semantics in terms of the operations in Span(RGraph) introduced in [5], and developed in [6, 7, 10].