Approximative analysis by process algebra with graded spatial actions

In this paper we propose a process algebra, CCSG, in which we can approximately analyze processes by neglecting unimportant dis- tant actions. Although many kinds of process algebra have already been proposed, there is a common problem that the number of feasible action sequences explosively increases with the number of concurrent processes. Therefore, an approximative approach is useful for large systems. We assume that each action has a grade which represents the importance. In CCSG, processes can be distributed in a space, and grades of observed actions decrease with distance. Hence observations of a system depend on the positions of observers. In this paper we give shift-(s) equivalence to relate observations at different positions, and give level- requivalence to relate an approximative observation and the complete observation.