Diposets and Concurrent System Semantics
John Davis, II

Modeling and designing concurrent systems requires a clear understanding of the types of relationships that exist between the components found in such systems. Two particularly important relationships found in concurrent systems are the order relation and the containment relation. The order relation represents the relative timing of component actions within a concurrent system and the containment relation facilitates human understanding of a system by abstracting a system's components into layers of visibility.

One major consequence of improper management of the order and containment relationships in a concurrent system is deadlock. Deadlock is an undesirable halting of a system's execution and is the most challenging type of concurrent system error to debug. The contents of this talk show that no methodology is currently available that can concisely, accurately and graphically model both the order and containment relations found in complex, concurrent systems. The result of the absence of a method suitable for modeling both order and containment is that analysis of concurrent systems is nearly impossible and the prevention of deadlock is extremely challenging.

I offer a solution to this problem by introducing the diposet. A diposet is a formal, mathematical structure that is similar in nature to a partially ordered set and is well suited to describing concurrent, computational systems. I define the diposet and show that it uses an order-centric approach that offers insight into the relative timing of events in a concurrent system and allows the specification of containment. The formal structure of a diposet is illustrated through the construction of several proofs and theorems and I provide real world examples to show that the diposet can model a wide variety of communication semantics including synchronous and asynchronous message passing.