  A quantitative model of concurrent interaction is introduced. The basic
objects are linear combinations of partial order relations, acted upon by a
group of permutations that represents potential non-determinism in
synchronisation. This algebraic structure is shown to provide faithful
interpretations of finitary process algebras, for an extension of the standard
notion of testing semantics, leading to a model that is both denotational (in
the sense that the internal workings of processes are ignored) and
non-interleaving. Constructions on algebras and their subspaces enjoy a good
structure that make them (nearly) a model of differential linear logic, showing
that the underlying approach to the representation of non-determinism as linear
combinations is the same.
