Analyze of Probabilistic Algorithms under Indeterministic Scheduler

In a distributed system, the environment is described by the scheduler (also called adversary or demon). Through an example related to stabilization, we show that a formal proof that does not use a formal definition of a scheduler is pointless. As a matter of fact, we show that the same algorithm, according to the scheduler, can be either correct or incorrect and in the cases where it is correct, can have different complexities. The paper is an attempt to better understand the meaning of proving a probabilistic algorithm in a indeterministic environment.