A model for distributed systems based on graph rewriting

Reviewer: D. John Cooke

In this lengthy paper the authors develop a graphical model to represent the activity of a certain type of distributed system, in which communication is via ports and no more than two processes are required to synchronize at any time via a common port. (This second restriction is introduced in order to keep matters simple but is not inherent in the underlying mathematics.) Basically, the primitive processes and the events to which they relate (the terminology used here is exactly the same as that found in the similarly named variant of Petri nets) give rise to a graph grammar that reflects both causal and communication links. Rewrite rules which ensure synchronization of appropriate events and processes are derived from the productions of the grammar. Execution of the distributed system is then mirrored by applications of these rules to give a sequence of expanding graphs. These represent events that happened in the past and processes that may be executed in the future. The initial configuration of a distributed system thus gives rise to sequences of possible behaviors which may be either finite or infinite. Moreover, the set of such sequences can be endowed with a metric derived from the length of the common truncation of two sequences, and the resulting space is complete. Several other interesting results and characterizations involving deadlocks, fairness, and the locally defined notion of success are derived. In its current form the work is mainly of theoretical interest, and then only to part of the computing community. Applying the work to temporal logic formalisms would seem to be a reasonable next move and should make it more approachable and applicable to both the development and the verification of distributed systems. The paper is logically structured. Aside from its informal second section, which is perhaps not as helpful as the authors believe, and some confusion in the diagrams (it is not always readily apparent which features and labels are mandatory or arbitrary), it reads well. The problem area is complex, and the constructions presented here reflect that complexity. Nevertheless, reading this paper will provide an extra perspective on distributed systems for those who study them.