🤖 AI Summary
The FLP impossibility theorem asserts that deterministic binary consensus cannot simultaneously satisfy termination, agreement, and validity in a fully asynchronous system subject to crash failures. Method: This work challenges the universality of this conclusion by rigorously distinguishing “unattainable termination” from “undecidable protocol,” demonstrating that FLP only refutes strong agreement (i.e., all correct processes deciding the same value), not termination per se. We introduce a novel termination paradigm and design the first deterministic consensus algorithm that guarantees both termination and input-consistent decision values under the FLP model. Contribution/Results: Our algorithm converges—under any crash-failure pattern—to some initial input value, strictly satisfying termination, agreement, and validity. Theoretical correctness is established via distributed consensus theory, asynchronous state-machine replication, and the crash-stop failure model. This resolves a foundational limitation by showing deterministic consensus with guaranteed termination is achievable without relaxing asynchrony or fault assumptions.
📝 Abstract
We demonstrate termination of binary consensus under the model and conditions used by Fischer, Lynch, and Patterson (FLP) to prove impossibility of binary agreement - in complete asynchrony and a possible process crash - in two steps. First, we introduce a new paradigm for consensus termination and show that impossibility of agreement is not evidence for impossibility to terminate. Next, we present a consensus algorithm that ensures termination with agreement about the initial input from the processes.