An algebra of processes (Q1096381)

The paper aims at developing a concept of distributed processes and operations which cover existing approaches, possibly avoiding their shortcomings. The concept of process is similar to that proposed by Brock and Ackerman and Staples and Nguyen. A process is characterized by the set of scenarios it can realize. The scenarios are defined in terms of messages, events, and the causal ordering of messages and events. The messages are supposed to occur in places as those in Petri nets. The places may be local in the process under consideration or shared with other processes. Processes may be combined as in Milner's CCS, but the only communication is by message passing, i.e. the communication of processes is represented by identifying some of the data one process produces and delivers to a place with the data another process takes up from this place and consumes. Since processes are concrete mathematical objects and the operations of combining them are concrete mathematical operations, an algebra of processes is developed such that properties of operations can be derived directly from definitions and do not need to be assumed as axioms. For example there exists the least upper bound of a set of processes with respect to a natural order, and it has the properties of indeterministic sum. The paper is concluded by a discussion on comparison with other approaches and by an example of proof of properties of a given process.