A Self-Stabilizing Hybrid Fault-Tolerant Synchronization Protocol

This paper presents a strategy for solving the Byzantine general problem for self-stabilizing a fully connected network from an arbitrary state and in the presence of any number of faults with various severities including any number of arbitrary (Byzantine) faulty nodes. The strategy consists of two parts: first, converting Byzantine faults into symmetric faults, and second, using a proven symmetric-fault tolerant algorithm to solve the general case of the problem. A protocol (algorithm) is also present that tolerates symmetric faults, provided that there are more good nodes than faulty ones. The solution applies to realizable systems, while allowing for differences in the network elements, provided that the number of arbitrary faults is not more than a third of the network size. The only constraint on the behavior of a node is that the interactions with other nodes are restricted to defined links and interfaces. The solution does not rely on assumptions about the initial state of the system and no central clock nor centrally generated signal, pulse, or message is used. Nodes are anonymous, i.e., they do not have unique identities. A mechanical verification of a proposed protocol is also present. A bounded model of the protocol is verified using the Symbolic Model Verifier (SMV). The model checking effort is focused on verifying correctness of the bounded model of the protocol as well as confirming claims of determinism and linear convergence with respect to the self-stabilization period.