Ready-trace semantics for concrete process algebra with the priority operator

The authors consider a process semantics intermediate between bi-simulation semantics and readiness semantics, called here ready-trace semantics. The advantage of this semantics is that, while retaining the simplicity of readiness semantics, it is still possible to augment this process model with the mechanism of atomic actions with priority (the theta operator). It is shown that in readiness semantics and failure semantics such as extension with theta is impossible. Ready-trace semantics is considered in the simple setting of concrete process algebra, that is: without abstraction (no silent moves), moreover for finite processes only. For such finite processes without silent moves a complete axiomatisation of ready-trace semantics is given via the method of process graph transformations