Courses/Distributed Systems

Distributed Systems

CS3.401

Prof. Kishore Kothapalli•Monsoon 2025-26•4 credits

Revision Notes/Unit 7 — Consensus & Byzantine Agreement

Unit 7 — Consensus & Byzantine Agreement

Reaching agreement among nodes that may fail. Crash-failure consensus: $f+1$ rounds, $(f+1) \cdot n^2$ messages. Byzantine bounds: $n \ge 3f+1$, $\ge f+1$ rounds. FLP impossibility in asynchronous systems. Lamport-Shostak-Pease oral-messages algorithm OM(m). Phase King — polynomial alternative with $n \ge 4f+1$. Three variants: Byzantine Agreement, Consensus, Interactive Consistency.

Crash Consensus + Byzantine Agreement (OM(m), Phase King) + FLP

20 min

Consensus = a group of nodes agree on a single value despite some being faulty. The difficulty depends on the failure model. **Crash-failure** (silent halts, no lies): solvable in $f + 1$ rounds with $n > f$ processes. **Byzantine** (arbitrary lying, conflicting messages): requires $n \ge 3f + 1$ and at least $f + 1$ rounds — and is **impossible in async systems** (FLP). Two flagship Byzantine algorithms: OM(m) (exponential messages, recursive) and Phase King (polynomial, needs more processes).