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In 1987, Schneider presented a general paradigm that provides a single proof of a number of fault tolerant clock synchronization algorithms. His proof was subsequently subjected to the rigor of mechanical verification by Shankar. However, both Schneider and Shankar assumed a condition Shankar refers to as a bounded delay. This condition states that the elapsed time between synchronization events (i.e., the time that the local process applies an adjustment to its logical clock) is bounded. This property is really a result of the algorithm and should not be assumed in a proof of correctness. This paper remedies this by providing a proof of this property in the context of the general paradigm proposed by Schneider. The argument given is a generalization of Welch and Lynch's proof of a related property for their algorithm. Miner, Paul S. Langley Research Center...
Schneider demonstrates that many fault tolerant clock synchronization algorithms can be represented as refinements of a single proven correct paradigm. Shankar provides mechanical proof that Schneider's schema achieves Byzantine fault tolerant clock synchronization provided that 11 constraints are satisfied. Some of the constraints are assumptions about physical properties of the system and cannot be established formally. Proofs are given that the fault tolerant midpoint convergence function satisfies three of the constraints. A hardware design is presented, implementing the fault tolerant midpoint function, which is shown to satisfy the remaining constraints. The synchronization circuit will recover completely from transient faults provided the maximum fault assumption is not violated. The initialization protocol for the circuit also provides a recovery mechanism from total system failure caused by correlated transient faults. Miner, Paul S. Langley Research Center ALGORITHMS; CIRCUITS; CLOCKS; FAULT TOLERANCE; SYNCHRONISM; CONVERGENCE; PROTOCOL (COMPUTERS); PROVING; SYSTEM FAILURES...
Existing fault-tolerant clock synchronization protocols are shown to result from refining a single clock synchronization paradigm. In that paradigm, a reliable time source periodically issues messages that cause processors to resynchronize their clocks. The reliable time source is aproximated by reading all clocks in the system and using a convergence function to compute a fault-tolerant average of the values read. The performance of a clock synchronization algorithm based on the paradigm can be quantified in terms of the two parameters that characterize the behavior of the convergence function used: accuracy and precision. Keywords: Byzantine agreement; Distrbiuted systems; Fault tolerance.