Characterizing contextual equivalence in calculi with passivation

We study the problem of characterizing contextual equivalence in higher-order languages with passivation. To overcome the difficulties arising in the proof of congruence of candidate bisimilarities, we introduce a new form of labeled transition semantics together with its associated notion of bisimulation, which we call complementary semantics. Complementary semantics allows to apply the well-known Howeʼs method for proving the congruence of bisimilarities in a higher-order setting, even in the presence of an early form of bisimulation. We use complementary semantics to provide a coinductive characterization of contextual equivalence in the HOπP calculus, an extension of the higher-order π-calculus with passivation, obtaining the first result of this kind. We then study the problem of defining a more effective variant of bisimilarity that still characterizes contextual equivalence, along the lines of Sangiorgiʼs notion of normal bisimilarity. We provide partial results on this difficult problem: we show that a large class of test processes cannot be used to derive a normal bisimilarity in HOπP, but we show that a form of normal bisimilarity can be defined for HOπP without restriction.