A Domain for Concurrent Termination: A Generalization of Mazurkiewicz Traces (Extended Abstract)

This paper generalizes the concept of Mazurkiewicz traces to a fuzzy description of a concurrent process, where a known preex is given in a rst component and a second alphabetic component yields necessary information about future actions. This allows to deene a good semantic domain where the concatenation is continuous with respect to the Scott-and to the Lawson topology. For this we deene the notion of ? and of-trace. We show various mathematical results proving thereby the soundness of our approach. Our theory is a proper generalization of the theory of nite and innnite words (with explicit termination) and of the theory of nite and innnite (real and complex) traces. We make use of trace theory, domain theory, and topology.