Partial orderings descriptions and observations of nondeterministic concurrent processes

A methodology is introduced for defining truly concurrent semantics of processes as equivalence classes of Labelled Event Structures (LES). The construction of a les providing the operational semantics of systems consists of three main steps. First, systems are decomposed into sets of sequential processes and a set of rewriting rules is introduced which describe both the actions sequential processes may perform and their causal relation. Then, the rewriting rules are used to build an occurrence net. Finally, the required event structure is easily derived from the occurrence net. As a test case, a partial ordering operational semantics is introduced first for a subset of Milner's CCS and then for the whole calculus. The proposed semantics are consistent with the original interleaving semantics of the calculus and are able to capture all and only the parallelism present in its multiset semantics. In order to obtain more abstract semantic definitions, new notions of observational equivalence on Labelled Event Structures are introduced that preserve both concurrency and nondeterminism.