The Simplex Family of Protocols

Simplex is a recent, deliberately minimalist BFT protocol design that traces its lineage back to Tendermint, stripping the protocol down to (in the authors’ framing) close to the theoretical minimum complexity for a partially-synchronous BFT protocol — this note groups the whole resulting research thread, since it’s one continuous story told across many posts. Covers the benign-fault and then Byzantine-fault variants in turn, 2-round BFT constructions in the Simplex style (including a variant tuned for $n=5f-1$ rather than the usual $n=3f+1$), concurrent 2-round-and-3-round variants, and a family of latency-reduced variants (C-Simplex, Kuplex, and an information-theoretic Kuplex needing no PKI). Also covers variants under granular synchrony (a finer-grained timing model than plain synchrony/partial synchrony), further partial-synchrony variants, structural analyses (“Deconstructing Simplex,” “From Simplex to Complex”), and fixed-view-schedule variants (including a faster one) that remove the need for view-change signaling entirely by agreeing on the leader schedule in advance.

Outline (TODO — flesh out each)

• From Tendermint to Simplex
• Benign Simplex
• From Benign Simplex to Byzantine Simplex
• 2-round BFT in Simplex style (general, and for $n=5f-1$)
• Concurrent 2-round and 3-round Simplex-style BFT
• C-Simplex and Kuplex — reduced bad-case latency
• Information-Theoretic Kuplex
• Concurrent 2/3-round BFT under granular synchrony
• Partial synchrony variants
• Deconstructing Simplex; from Simplex to Complex
• Simplex (and Fast Simplex) on a fixed view schedule