A Truly Concurrent Process Semantics over Multi-Pomsets of Consumable Resources

This paper develops a truly concurrent semantical approach, whereby concurrency is notionally independent of nondeterminism, that allows describing the deterministically concurrent behaviour of recursive processes accessing consumable resources. The process semantics is based on the new coherently complete and prime algebraic domains of real and complex multi-pomsets. The process language that we study contains several deterministic quantitative process operators, namely a renaming, a hiding, a restriction, a serial and a parallel operator, as well as a recursion operator. The displayed deterministic structural operational machine engenders a linear and a complex operational semantics. A compositional denotational semantics is constructed, which uses a functional domain over environments of complex multi-pomsets. The robustness of the presented semantical work is established by proving that the denotational semantics is fully abstract with respect to both linear and complex operational semantics.