Bisimulation indexes and their applications

• Authors: Mingsheng Ying
• Venue: Theoretical Computer Science
• Year: 2002

Bisimulation expresses the equivalence of processes whose external actions are identical. Sometimes we may meet two processes which are not exactly bisimilar but more or less bisimilar in the sense that whenever a process makes an action the other can make an action different from but very similar to the action performed by the first one. To describe this kind of looser bisimulations we propose the concept of bisimulation index in a labelled transition system and give its various properties, especially those properties related to the operations of transition systems. Furthermore, we establish a modal logical characterization of bisimulation indexes. This characterization is a generalization of Hennessy-Milner logic. We study strong and weak bisimulation indexes in the basic asynchronous process calculus, and some of their fundamental properties are derived. Bisimulation indexes are not substitutive under composition. To overcome this defect we introduce an approximate communication rule to replace the original rule in process calculus. This enables us to recover some useful properties of composition with respect to bisimulation indexes. Finally, we present three examples in timed CCS and real time ACP to demonstrate the usage of bisimulation indexes in the analysis of real time systems. These examples show that bisimulation indexes are suitable formal tools for describing approximate implementations of real time systems.