Specifying Confluent Processes

We address the problem of specifying concurrent processes that can make local nondeterministic decisions without affecting global system behavior—the sequence of events communicated along each inter-process communication channel. Such nondeterminism can be used to cope with unpredictable execution rates and communication delays. Our model resembles Kahn’s, but does not include unbounded buffered communication, so it is much simpler to reason about and implement. After formally characterizing these so-called confluent processes, we propose a collection of operators, including sequencing, parallel, and our own creation, confluent choice, that guarantee confluence by construction. The result is a set of primitive constructs that form the formal basis of a concurrent programming language for both hardware and software systems that gives deterministic behavior regardless of the relative execution rates of the processes. Such a language greatly simplifies the verification task because any correct implementation of such a system is guaranteed to have the same behavior, a property rarely found in concurrent programming environments.