Characterizing contextual equivalence in calculi with passivation

We study the problem of characterizing contextual equivalence in higher-orderlanguages with passivation. To overcome the difficulties arising in the proofof congruence of candidate bisimilarities, we introduce a new form of labelledtransition semantics together with its associated notion of bisimulation, whichwe call complementary semantics. Complementary semantics allows to applythe well-known Howe’s method for proving the congruence of bisimilarities ina higher-order setting, even in presence of an early form of bisimulation. Weuse complementary semantics to provide a coinductive characterization of con-textual equivalence in the HOπP calculus, an extension of the higher-order π-calculus with passivation, obtaining the first result of this kind. We then studythe problem of defining a more effective variant of bisimilarity that still char-acterizes contextual equivalence, along the lines of Sangiorgi’s notion of normalbisimilarity. We provide partial results on this difficult problem: we show thata large class of test processes cannot be used to derive a normal bisimilarity inHOπP, but we show that a form of normal bisimilarity can be defined for HOπPwithout restriction.