Abstract
In this paper, we consider a generalisation of a result due to the author which describes the way in which Mazurkiewicz trace languages serve to represent systems of labelled partial orders, as used in non-interleaving semantics of parallelism. The generalisation extends the class of partial order systems to exclude only a form of non-determinism. Their representation is in terms ofa generalisation of traces, also due to Mazurkiewicz, called multi traces.

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