An abstraction method of behaviors for process algebra

In CCS, Milner defined the notion of Strong and Weak Bisimulations for behavioral equivalence between two processes or systems. However the notion has not been studied further in the perspective of abstraction for such behaviors in process algebra. In some sense, weak bisimulation could be interpreted as a kind of behavior equivalence between two processes at the certain degree of abstraction, based on observability. Here we noticed the possibility of representing such observable behaviors with a certain structure of abstraction and verify a number of behavioral equivalences in the structure. In the paper, such possibility has been realized with a new concept of Behavior Ontology. In the ontology, actions can be defined as an interaction between two processes or systems, and, further, behaviors can be defined as a sequence of such actions. Since some actions between the behaviors can be overlapped in some structural way, the behaviors can be organized in a lattice structure, namely, Behavior Lattice. Consequently, the lattice reveals certain levels of observability of the behaviors, based on degree of abstraction. From the lattice, a strong bisimulation and its weak bisimulations can be detected visually. The comparative study shows that the ontology is very effective and efficient for representing such abstract behaviors and verifying strong and weak bisimulations in a lattice structure. The ontology can be considered as one of the unique and innovative structure to represent such behaviors in a hierarchical structure of abstraction.