CSP refusal set

A CSP refusal set is a set $X$ of visible CSP events that a process can decline together in a stable state. Stability excludes an enabled internal transition. Pairing $X$ with a preceding trace gives a failure observation; different internal resolutions after the same trace can produce different refusal sets.^[ref]

For an event alphabet $\{a,b\}$, a state offering only $a$ can refuse $\{b\}$ but cannot refuse $\{a\}$. Every subset of a possible refusal is also possible. In a model without a separate successful-termination event, refusing the entire event alphabet signals deadlock. Refusals therefore distinguish a missing offer from an event merely not selected by the environment.