Structural and Behavioural Equivalences of Networks

We define an algebraic language for networks of synchronously communicating processes. A node in the Network may have several ports; a port is either external to the whole network or connected through a link to another port. The language contains two types of operations: parallel composition of two networks, and interlinking of two external ports within a network. We interpret this language in two ways: first we give a structural semantics, where terms are mapped to graphs representing the structure of networks, and second we give a behavioural semantics, where terms are mapped to behaviour schemes. A schema corresponds to a behaviour parameterised on the behaviours of the network nodes. These semantics give rise to structural and behavioural equivalences. We compare the equivalences and give sound and complete axiomatisations