A Truly Concurrent Process Calculus over Recyclable Resources

In this paper we present a truly concurrent semantics for deterministic concurrent recursive processes accessing quantified recyclable resources. The process semantics is built upon the new coherently complete and prime algebraic domain of continued multi-pomsets, which is a quantitative version of the domain of complex resource pomsets. The CSP-like process language that we study contains several deterministic quantitative process operators, namely hiding, restriction, sequential, serial and parallel, as well as an observable recursion. A deterministic structural operational machine is displayed that allows extracting a linear and a continued operational semantics. The denotational semantics is naturally defined on continued multi-pomsets for all finitary operators and lifted to a functional domain over environments modelling recursion. The robustness of the present semantical work is demonstrated by proving that the denotational semantics is fully abstract with respect to the linear and the continued operational semantics and by relating it via observation to bisimilarity.