The expressive power of parallelism

We explore an algebraic language for networks consisting of a xed number of reactive units, communicating synchronously over a xed linking structure. The language has only two operators: disjoint parallelism, where two networks are composed in parallel without any interconnections, and linking, where an interconnec-tion is formed between two ports. The intention is that these operators correspond to the primitive steps when constructing networks, and that they therefore are conceptually simpler than the operators in existing process algebras. We investigate the expressive power of our language. The results are: (1) Deenability of behaviours: with only three simple processing units, every nite-state behaviour can be constructed. (2) Deenability of operators: we characterise the network operators which are deenable within the language; these turn out to include most operators previously suggested for describing parallelism. Our results hold for any congruence between trace equivalence and observation equivalence.