Denotational semantics for timed testing

In this paper we present a denotational semantics for a timed process algebra, which is fully abstract with respect to the must testing semantics previously developed [Lla96,LdFN96]. The domain of semantic processes is made up of consistent sets of barbs, which generalize the notion of acceptance sets, in such a way that the actions that are offered but not taken in each state are also recorded. the main difficulty when defining this denotational semantics has been that the natural ordering between semantic processes cannot be proved to be complete. So an alternative stronger complete ordering has to be considered, which is proved to be consistent with the original one, in the sense that lubs of chains with respect to the new ordering are also lubs with respect to the original one.