Divergence in Testing and Readiness Semantics

 Michele Boreale1, Rocco De Nicola2, Rosario Pugliese2,
1 Dipartimento di Scienze dell'Informazione, Universita' di Roma ``La Sapienza''
2 Dipartimento di Sistemi e Informatica, Universita' di Firenze

Many variants of must-testing equivalence 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 equivalence is one of such variants, that naturally pops up when studying the behavioural pre--congruences induced by certain basic observables. Here, we study the relationships between safe testing and Olderog's readiness semantics, an equivalence induced by a natural process logic. We show that safe testing is finer than readiness equivalence, and coincides with a refinement of this semantics, obtained by a fine tuning of Olderog's definition. For both safe testing and the original readiness semantics we propose simple complete axiomatizations, which permit a fuller appreciation of these equivalences and of their similarities.