Analysis of an Intentional Fault Which Is Undetectable by Local Checks under an Unfair Scheduler

Abstract

We consider a malicious unfair adversary which generates an undetectable fault by local checks, called an intentional fault. Though the possibility of such a fault has ever been suggested, details of its influence and handling are unknown. We assume the intentional fault in a self-stabilizing mutual exclusion protocol, a hybrid of previously proposed ones that complement each other. In the hybrid protocol, we can cope with the fault by using optional strategies, whether or not sending a minor token, which plays a role of preventing the contamination from spreading. We construct a payoff matrix between a group of privileged processes and an adversary, and consider a multistage two-person zero sum game. We interpret the game in two ways: whether it continues or replays the game after an ME(mutual exclusion)-violating repair, in which more than one unexpected privileges are given. For each case, we evaluate the ability of malicious unfair adversary by using a mixed strategy. Our idea is also considered as a general framework for strengthening an algorithm against an intentional fault.