APPROXIMATING TRACES

In order to give a semantics to concurrent processes we need a model h aving some good mathematical properties. To this end we generalize (in finite) Mazurkiewicz traces by adding some alphabetical information co ncerning the possible continuations of a process. This allows to defin e an approximation order compatible with the composition. We obtain a prime algebraic and coherently complete domain where the compact eleme nts are exactly the finite approximations of processes. The compositio n is shown to be monotone and U-continuous. We define a suitable metri c which induces the Lawson topology and which yields a compact metric space being therefore complete, The finite approximations of processes form a dense and open subset and the composition is (uniformly) conti nuous. A preliminary version of this work appeared in [7].