A Sufficient Condition for the Observational Equivalence of Processes

The article deals with the problem of proving observational equivalence for the class of computational processes called processes with message passing. These processes can execute actions of the following forms: sending or receiving of messages, checking logical conditions and updating values of internal variables of processes. Our main result is a theorem that reduces the problem of proving observational equivalence of a pair of processes with message passing to the problem of finding formulas associated with pairs of states of these processes, satisfying certain conditions that are associated with transitions of these processes. This reduction is a generalization of Floyd’s method of flowchart verification, which reduces the problem of verification of flowcharts to the problem of finding formulas (called intermediate assertions) associated with points in the flowcharts and satisfying conditions, corresponding to transitions in the flowcharts. The above method of proving observational equivalence of processes with message passing is illustrated by a sliding window protocol verification.