On Bisimulation Theory in Linear Higher-Order π-Calculus

Higher-order process calculi are an important branch of process model for its significance in both theory and practice. In this paper, we establish new results on bisimulation theory in linear higher-order pi-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 first-order bound output clause in local bisimulation by harnessing the congruence properties.