Divergence in testing and readiness semantics

Many variants of must-testing semantics have been put forward that are equally sensitive to deadlock, but differ for the stress they put on divergence, i.e. on the possibility for systems of getting involved in infinite internal computations. Safe-testing is one such variant, that naturally pops up when studying the behavioural pre-congruences induced by certain basic observables. Here, we study the relationship between safe-testing and Olderog's readiness semantics, a semantics induced by a natural process logic. We show that safe-testing is finer than readiness, and coincides with a refinement of readiness obtained by tuning Olderog's definition. For both safe-testing and the original readiness semantics we propose simple complete axiomatizations, which permit a fuller appreciation of their similarities and differences.