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Verification of fault-tolerant distributed protocols is an immenselydifficult task. Often, in these protocols, thresholds on set cardinalities areused both in the process code and in its correctness proof, e.g., a process canperform an action only if it has received an acknowledgment from at least halfof its peers. Verification of threshold-based protocols is extremelychallenging as it involves two kinds of reasoning: first-order reasoning aboutthe unbounded state of the protocol, together with reasoning about sets andcardinalities. In this work, we develop a new methodology for decomposing theverification task of such protocols into two decidable logics: EPR and BAPA.Our key insight is that such protocols use thresholds in a restricted way as ameans to obtain certain properties of "intersection" between sets. We define alanguage for expressing such properties, and present two translations: to EPRand BAPA. The EPR translation allows verifying the protocol while assumingthese properties, and the BAPA translation allows verifying the correctness ofthe properties. We further develop an algorithm for automatically generatingthe properties needed for verifying a given protocol, facilitating fullyautomated deductive verification. Using this technique we have verified severalchallenging protocols, including Byzantine one-step consensus, hybrid reliablebroadcast and fast Byzantine Paxos.

Verification of Threshold-Based Distributed Algorithms by Decomposition to Decidable Logics