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This theoretical analysis demonstrates limitations of deterministic protocols for consensus in distributed systems, suggesting significant implications for protocol design.
The classic Fischer, Lynch, and Paterson impossibility proof [7, 12] demonstrates that any deterministic protocol for consensus in either a message-passing or shared-memory system must violate at least one of termination, validity, or agreement in some execution. But it does not provide an efficient procedure to find such a bad execution.
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Aspnes et al. (2026) studied this question.
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