This paper carries out a systematic investigation into the bisimulation lattice of asymmetric chi calculus with a mismatch combinator. It is shown that all the sixty three L bisimilarities collapse to twelve distinct relations and they form a bisimulation lattice with respect to set inclusion. The top of the lattice coincides with the barbed bisimilarity.
A schematic law dealing with localization operator is proposed for pi calculus. It is shown that the law renders the use of distinction unnecessary in the axiomatic theory of open congruence.
The ehi calculus is a model of mobile processes. It has evolved from the pi-calculus with motivations from simplification aml communication-as-cut-eliminatinn. This paper studies the ehi calculus in the framework incorporating asymmetric communication. The major feature of the calculus is the identification of two actions： x/x and τ. The investigalion on the barbed bisimilarity shows how the property affects the observational theory. Based on the definition of the barbed bisimilarity, the simulation properties of the barbed bisimilarity are studied. It shows that the algebraic properties of the barbed bisimiilarity have changed greatly compared with the chi calculus.Although the definition of the barbed bisimilarity is very simple, the properly of closeness under contexts makes it difficuh to understand the barbed bisimilarity directly. Therefore an open style definition of the barbed bisimilarity is given, which is a context free description of barbed bisimilarity. Its definition is complex, but it is a well-behaved relation for it coincides with the barbed bisimilarity. It also helps to build an axiomatization system for the bathed congruence. Besides the axioms for the strong barbed bisimilarity, the paper proposes a new tau law and four new update laws for the barbed congruence. Both the operational and algebraic properties of the enriched calculus improve the understanding of the bisimulation behaviors of the model.
