Distributed Implementation of CCS

A distributed semantics for CCS is given by implementing Milner's Calculus of Communicating Systems onto a simpler calculus of Place/Transition Petri Nets. The net calculus, called SCONE+, is an extension of SCONE [GM90], which has the finer grained operation of local nondeterministic choice, with some operations for modelling restriction and relabelling. In this way, full CCS can be given a net implementation in a purely algebraic way. The complex CCS operation of global nondeterminism is implemented by means of a suitable mapping, which makes explicit the fact that certain CCS transitions are implemented as SCONE+ computations to be executed atomically. To this aim, CCS and SCONE+ are given an operational semantics in algebraic form. In this way, the mapping from CCS transitions to SCONE+ computations becomes simply an algebraic morphism, which can be interpreted as a denotational semantics for CCS having SCONE+ as interpretation domain. The semantics of CCS obtained by quotienting the CCS transition system w.r.t. the implementation mapping is equivalent to the concurrent semantics by “permutation of transitions”, as proposed in [BC90, FM90].

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