Trade-offs in True Concurrency: Pomsets and Mazurkiewicz Traces

Abstract

We compare finite pomsets and Mazurkiewicz traces, two models of true concurrency which generalize strings. We show that Mazurkiewicz traces are equivalent to a restricted class of pomsets. The restrictions lead to extra structure, with results analogous to the differences between simply typed and untyped languages. For example, traces are consistently complete in the prefix order, while pomsets are not; also, traces can be distinguished by observing sequences of actions, in contrast to the elaborate scheme required for distinguishing pomsets. Finally, we discuss the operations of sequential and parallel composition in the two models. This is part of an ongoing effort to relate models of concurrency.