Two complete axiom systems for a theory of communicating sequential processes

In Hoare, Brookes and Roscoe (1981) an abstract version of Hoare's CSP is defined and a denotational somantics based on the possible fallures of processes is given for it. This semantics induces a natural preorder on processes. We define formally this preoreder and prove that it can be characterized as the smal1est relation satisfying a particular set of axioms. The characterization sheds lghts on problems arising from the way divergence and underspecification are handled. After small changes to tho semantic domains we propose a new semantics which Is closer to the operational Intuitions and suggests a possible solution to the above problems.Finallywe give an axiomatic characterization for the equivalence Induced by the new semantics whlch lead to fully abstract models in the sense of Scott.