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README.md

TLA+ Formal Verification for HotStuff-2

Formal specification and verification of the HotStuff-2 consensus protocol using TLA+ model checking.

Verification Status

PRODUCTION-READY: Formally verified for safety and liveness, including Byzantine fault tolerance.

Completed Verification Runs

Configuration Spec States Distinct Runtime Status
Smoke Spec 15K 5K 4s PASS
Safety-Standard Spec 1.18M 358K 22s PASS
Liveness-Basic FairSpec 65K 20K 23s PASS
Liveness-Deep FairSpec 1.32M 397K 9.2min PASS
Fault-Tolerance FairSpec 26K 10K 13s PASS

Total: 2.6M+ states explored, 790K+ distinct states, all properties verified.

Verified Properties

Safety Invariants (12 total)

Core Safety (all configs)

  1. TypeInvariant - All variables maintain correct types
  2. AgreementInvariant - No two replicas commit different blocks at same height
  3. ValidityInvariant - Only proposed blocks can be committed
  4. QCIntegrityInvariant - Quorum certificates require 2f+1 valid votes
  5. ForkFreedomInvariant - No conflicting blocks at same height with QCs
  6. CommitChainInvariant - Committed blocks form valid chain from genesis
  7. NoDoubleVoteInvariant - Replicas vote at most once per view
  8. SingleProposalInvariant - At most one proposal per view
  9. VotesSubsetReplicasInvariant - All votes from valid replicas
  10. UniqueQCPerViewInvariant - At most one QC per view
  11. HonestAgreementInvariant - Honest replicas never commit conflicting blocks
  12. HonestValidityInvariant - Honest commits are valid

Constant-Level Assumptions (verified at model init via ASSUME)

  • FaultToleranceAssumption - |Faulty| <= f (BFT assumption holds)
  • QuorumIntersectionProperty - Any two quorums share an honest replica

Liveness Properties (4)

Verified under weak fairness assumptions (FairSpec):

  1. EventuallyCommit - Eventually some block is committed
  2. EventualProgress - The committed set eventually grows
  3. ViewEventuallyCompletes - Every view either forms a QC or times out
  4. EventualViewSync - All replicas eventually reach the same view

Quick Start

Prerequisites

Install TLA+ Toolbox from https://github.com/tlaplus/tlaplus/releases

Running Verification

  1. Open TLA+ Toolbox
  2. File → Open Spec → Add Module → hotstuff2.tla
  3. TLC Model Checker → New Model
  4. Configure using one of the .cfg files below
  5. Run Model

Configuration Files

File Purpose Faulty Runtime
hotstuff2_smoke.cfg Quick smoke test - ~4s
hotstuff2_safety_standard.cfg Safety verification {} ~23s
hotstuff2_liveness_basic.cfg Liveness (basic) {} ~25s
hotstuff2_liveness_deep.cfg Liveness (deep) - ~10min
hotstuff2_fault_tolerance.cfg Fault tolerance {4} ~14s

The hotstuff2_fault_tolerance.cfg configuration models f=1 crash fault (replica 4 never participates). This tests the critical BFT liveness property that honest replicas make progress despite faults.

TLC Command Line

# Safety verification
java -XX:+UseParallelGC -Xmx4G -cp tla2tools.jar tlc2.TLC \
  -config hotstuff2_safety_standard.cfg \
  -workers auto \
  hotstuff2.tla

# Liveness verification
java -XX:+UseParallelGC -Xmx8G -cp tla2tools.jar tlc2.TLC \
  -config hotstuff2_liveness_deep.cfg \
  -workers auto \
  hotstuff2.tla

Model Parameters

All configurations use n=4 replicas (f=1, quorum=3):

Config MaxView MaxHeight Faulty Spec Invariants Liveness
Smoke 2 2 {} Spec 12 -
Safety-Standard 4 3 {} Spec 12 -
Liveness-Basic 3 2 {} FairSpec 12 4
Liveness-Deep 4 3 {} FairSpec 12 4
Fault-Tolerance 4 3 {4} FairSpec 12 4

Notes:

  • With Faulty = {}, HonestAgreementInvariant equals AgreementInvariant
  • The fault config (Faulty = {4}) tests liveness with one crashed replica

Implementation Mapping

See IMPLEMENTATION_MAPPING.md for detailed TLA+ to Go code mapping.

Files

File Description
hotstuff2.tla Main TLA+ specification (~450 lines)
hotstuff2_smoke.cfg Smoke test configuration
hotstuff2_safety_standard.cfg Safety verification configuration
hotstuff2_liveness_basic.cfg Liveness verification (basic)
hotstuff2_liveness_deep.cfg Liveness verification (deep)
hotstuff2_fault_tolerance.cfg Fault tolerance verification (f=1 crash)
IMPLEMENTATION_MAPPING.md TLA+ to Go implementation mapping

Fault Model

The specification supports Byzantine fault tolerance verification via the Faulty constant:

CONSTANTS
    Replica,    \* Set of all replica IDs
    Faulty,     \* Set of faulty replica IDs (subset of Replica)
    ...

Honest == Replica \ Faulty

Crash Fault Model

The current fault model is crash faults (fail-stop):

  • Faulty replicas never send messages (no votes, no proposals, no NEWVIEWs)
  • Faulty replicas never update state
  • This models the worst case for liveness: maximum unresponsive nodes

BFT Assumption

The spec enforces |Faulty| <= f where f = (n-1)/3. For n=4:

  • f = 1
  • Quorum = 2f+1 = 3
  • With 1 faulty replica, 3 honest replicas must be able to make progress

Critical Fix: Leader's Implicit Vote

Without the leader's vote, liveness fails under faults:

  • 3 honest replicas, 1 is leader
  • Only 2 honest non-leaders can vote
  • 2 < 3 (quorum) = deadlock

With the leader's implicit vote (added in LeaderPropose):

  • Leader votes for its own proposal
  • 3 votes possible: leader + 2 honest non-leaders
  • 3 >= 3 (quorum) = progress

This fix is implemented in both TLA+ (hotstuff2.tla:179-205) and Go (hotstuff2.go:653-662).

Protocol Overview

The TLA+ specification models HotStuff-2 as an asynchronous message-passing system:

State Variables

  • view[r] - Current view for each replica
  • lockedQC[r] - Locked QC (safety mechanism)
  • highQC[r] - Highest QC seen
  • committed[r] - Set of committed blocks
  • network - Persistent message set (PROPOSE, VOTE, NEWVIEW)

Actions

  • LeaderPropose - Leader broadcasts proposal with justification QC
  • ReplicaVote - Replica votes if proposal satisfies SafeNode rule
  • LeaderFormQC - Leader forms QC from 2f+1 votes
  • ReplicaUpdateOnQC - Replica updates state on seeing QC
  • ReplicaTimeout - Replica advances view on timeout
  • LeaderProcessNewView - New leader proposes after collecting NEWVIEWs

SafeNode Rule (Core Safety Mechanism)

SafeNodeRule(r, block, qc) ==
    \/ lockedQC[r] = Nil
    \/ (qc /= Nil /\ blockView[qc] > blockView[lockedQC[r]])
    \/ IsAncestor(lockedQC[r], block)

References

Last Verified: 2025-11-27
Status: Production-ready
Coverage: 790K distinct states, 12 safety invariants, 4 liveness properties