Basic Observables for Probabilistic May Testing

The definition of behavioural preorders over process terms as the maximal (pre-)congruences induced by basic observables has proven to be a useful technique to define various preorders and equivalences in the non-probabilistic setting. In this paper, we consider probabilistic observables to define an observational semantics for a probabilistic process calculus. The resulting pre-congruence is proven to coincide with a probabilistic may preorder, which, in turn, corresponds to a natural probabilistic extension of the may testing preorder of De Nicola and Hennessy.