On Bisimulation Theory in Linear Higher-Order pi-Calculus

Higher-order process calculi have been receiving much attention in recent years for its significance in both theory and practice. Work on bisimulations has never ceased evolving, typically represented by Thomsen and Sangiorgi for their work on bisimulation theory and encoding to and from first-order process calculi. Fu puts forth linear higher-order π-calculus, and makes improvement to previous work on bisimulation and builds a sound and complete equation system by exploiting linearity of processes, which takes resource sensitiveness into account. In this paper, we establish some recent result on bisimulation theory in linear higher-order π-calculus. By exploiting the properties of linear higher-order processes, we work out two simpler variants than local bisimulation, which is an intuitive observational equivalence. We prove that they both coincide with local bisimilarity. The first variant, called local linear bisimulation, simplifies the matching of higher-order input and higher-order output based on the feature of checking equivalence with some special processes (in input or output) instead of general ones. The second variant, called local linear variant bisimulation, rewrites the firstorder bound output clause in local bisimulation in some more suitable form for some application on it, by harnessing the congruence properties. We also mention some future work in the conclusion.