Operational and denotational semantics for the box algebra

This paper describes general theory underpinning the operational semantics and the denotational Petri net semantics of the box algebra including recursion. For the operational semantics, inductive rules for process expressions are given. For the net semantics, a general mechanism of refinement and relabelling is introduced, using which the connectives of the algebra are defined. The paper also describes a denotational approach to the Petri net semantics of recursive expressions. A domain of nets is identified such that the solution of a given recursive equation can be found by fixpoint approximation from some suitable starting point. The consistency of the two semantics is demonstrated. The theory is generic for a wide class of algebraic operators and synchronisation schemes.