Application of TLRO to refute an incorrect mutual exclusion algorithm

Abstract

Modeling of iterative commands in a concurrent process is difficult because the termination depends on the states of different processes. In this paper a Temporal Logic Related to Observation (TLRO)-based modeling of the same is considered. For simplicity we restrict ourselves to 'while do' construct only. Using a commonsense scenario it is shown that the construct may be described by a set of three state transition rules. In a concurrent system the termination condition is determined by the states of different processes. To ensure termination, therefore, temporal ordering of the executions of different state transition rules at different processes needs to be investigated. For this purpose we prove two theorems. The entire derivation is then used to refute a well known incorrect mutual exclusion algorithm. A counter example for the algorithm could be derived during this exercise. This is an improvement over our earlier effort that used the weakest precondition calculus as a modeling tool.