Verification of a Byzantine-Fault-Tolerant Self-Stabilizing Protocol for Clock Synchronization

Abstract

Abstract-This paper presents the mechanical verification of a simplified model of a rapid Byzantine-fault-tolerant selfstabilizing protocol for distributed clock synchronization systems. This protocol does not rely on any assumptions about the initial state of the system except for the presence of sufficient good nodes, thus making the weakest possible assumptions and producing the strongest results. This protocol tolerates bursts of transient failures, and deterministically converges within a time bound that is a linear function of the self-stabilization period. A simplified model of the protocol is verified using the Symbolic Model Verifier (SMV) [1]. The system under study consists of 4 nodes, where at most one of the nodes is assumed to be Byzantine faulty. The model checking effort is focused on verifying correctness of the simplified model of the protocol in the presence of a permanent Byzantine fault as well as confirmation of claims of determinism and linear convergence with respect to the self-stabilization period. Although model checking results of the simplified model of the protocol confirm the theoretical predictions, these results do not necessarily confirm that the protocol solves the general case of this problem. Modeling challenges of the protocol and the system are addressed. A number of abstractions are utilized in order to reduce the state space.

A Byzantine-Fault Tolerant Self-stabilizing Protocol for Distributed Clock Synchronization Systems

“…The algorithm in [11] is called the Byzantine self-stabilization pulse synchronization (BSS-Pulse-Synch) protocol. A flaw in BSS-Pulse-Synch protocol was found and documented in [12]. The biologically inspired Pulse Synchronization protocol in [10] has claims of self-stabilization, but no mechanized 1 proofs are provided.…”

A self-stabilizing hybrid fault-tolerant synchronization protocol

“…The protocol described in this paper is fairly subtle and must necessarily cope with many kinds of timing behaviors. Model checking has been used to explore and verify distributed algorithms but also faces certain difficulties [16], [24]- [26]. One of the foremost challenges is a realistic representation of time as a continuous variable.…”

“…Two Byzantine-fault-tolerant self-stabilizing protocols for distributed systems were reported in [14] and [15]. Instances of these protocols were demonstrated via mechanical verification to self-stabilize from any state, in the presence of at most one permanent Byzantine faulty node, and to deterministically converge in linear time with respect to the synchronization period [16]. These protocols, however, do not solve the general case of the problem in the presence of multiple Byzantine faults [15].…”