Theχcalculusisamodelofconcurrentandmobilesystems.Itemphasizesthatcommunicationsareinformationexchanges.Inthepaper,twoconstructionsareincorporatedintotheframeworkofthechicalculus,whichareasymmetriccommunicationandmismatchconditionwidelyusedinapplications.Sincethebarbedbisimilarityhasproveditsgeneralityandgaineditspopularityasaneffectiveapproachtogeneratingareasonableobservationalequivalence,westudyboththeoperationalandalgebraicpropertiesofthebarbedbisimilarityinthisenrichedcalculus.Theinvestigationsupportsanimprovedunderstandingofthebisimulationbehaviorsofthemodel.Italsogivesageneralpictureofhowthetwoconstructionsaffecttheobservationaltheory.
