Operational and Denotational Semantics for the Box Algebra

This paper describes general theory underpinning the operational semantics and the denota-tional 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 re-nement and relabelling is introduced, using which the connectives of the algebra are deened. The paper also describes a denotational approach to the Petri net semantics of recursive expressions. A domain of nets is identiied such that the solution of a given recursive equation can be found by xpoint 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.