PARTIAL ORDER MODELS OF CONCURRENCY AND THE COMPUTATION OF FUNCTIONS.

The authors describe an abstract approach, based on structures of partially ordered events, for specifying and analyzing concurrent processes. Within this approach, one framework is the pomset model. Another is based on structures called prossets (preorder specification sets) which include, in addition to the less than -relation, a relation for denoting simultaneity of events. Some of the results apply to both, with almost identical proofs; others necessitate the use of prossets. They show how, within a framework of this kind, general abstract definitions can be given to concepts such as: fairness, input event, a location of the process (which can store members of some given, arbitrary complete partial order, input-location, and the relation computed by the process in a given location. Process composition and formation of loops are defined using a fusion operation, by which several locations are fused into one. G. Kahn's (1974) network semantics turns out to be a rather particular case, derived from an abstract theorem which establishes a connection between operations on processes and the least fixpoint operator on the functions defined by them.