Broadcasting with Priority

Adding priorities to CCS is di cult, and involves two-stage operational semantics or other complications. By contrast, priorities can be added very simply to a calculus of broadcasting systems (CBS). The reason is the input/output distinction made in CBS, with output actions being autonomous. Priority makes sense only for autonomous actions. As in unprioritised CBS, both strong and weak bisimulation are congruences, and capture the intuitively desired equivalences. CBS is also a powerful and natural language, o ering an interesting new programming paradigm. Several examples show that priorities extend both the power and the paradigm. The public address system at an airport can give bomb alerts, say, priority over ight announcements. Everyone hears messages read out over the system, but individual responses vary. Priority assignment cannot depend on the actual public responses to the contending messages, even if expectations about responses play a role. Priority here is only a matter of choosing between the messages themselves. Priorities in the marketplace are more complex, because buyer and seller must agree for a sale to take place. Sellers' minimum prices and buyers' maximum prices must be met, but further preferences for advantageous prices are not relevant unless there are competing parties to do business with. A broker arranging sales that respect everybody's priorities has a harder task than the announcer at the airport. The handshake (or rendezvous) model of communication is similar to the market model. An indication of the di culty of respecting priorities in this model is the \priority inversion" problem in Ada [BA90]. This model is also predominant in process calculus. The several papers [BBK85, CH88, CW91] that add priority to process calculus have all used this model, and therefore su er from the broker's di culties. In [CH88], an a priori semantics works out what might happen, and a second stage works out what actually happens. In [CW91], transitions are predicated on what the environment can do. This paper adds priorities to a calculus of broadcasting systems (CBS) [Pra93c]. The resulting CBS with priorities (PCBS) is strikingly simple, and compares very favourably with CCS with priorities. This con rms the intuition above, since the