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🔬 Complete Formal Verification - Alpenglow Consensus Protocol
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‎alpenglow-formal-verification/Alpenglow.cfg‎

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CONSTANT
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NumValidators = 4
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MaxSlots = 5
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StakeWeights <- StakeWeightsFcn
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StakeWeightsFcn == [v \in 1..4 |-> 25]
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SPECIFICATION Spec
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PROPERTIES
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Safety_NoConflictingBlocks
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Safety_CertificateUniqueness
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Safety_ChainConsistency
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Liveness_Progress
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Liveness_FastPath
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Liveness_BoundedFinalization
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Resilience_ByzantineSafety
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Resilience_NonResponsiveLiveness
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Resilience_PartitionRecovery
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CHECK_DEADLOCK FALSE
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POSTCONDITION
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TLCGetAndReportStats

‎alpenglow-formal-verification/Alpenglow.tla‎

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---- MODULE Alpenglow ----
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(*
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Formal Verification of Solana's Alpenglow Consensus Protocol
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Using TLA+ for machine-checkable proofs
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Wallet for bounty: 8UMZuLfZ9VvGq4YvBUh5TW7igTPma5HbEM5J7YSBGbMR
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*)
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EXTENDS Naturals, FiniteSets, Sequences, TLC
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CONSTANT
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\* Number of validators
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NumValidators,
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\* Maximum slots to simulate
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MaxSlots,
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\* Stake distribution (total stake = 100)
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StakeWeights
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ASSUME
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/\ NumValidators \in 4..10 \* Small configurations for model checking
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/\ MaxSlots \in 5..20
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/\ StakeWeights \in [1..NumValidators -> 1..50]
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VARIABLES
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\* Current slot
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currentSlot,
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\* Blocks proposed per slot
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blocks,
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\* Votes cast by validators
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votes,
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\* Certificates generated
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certificates,
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\* Finalized blocks
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finalizedBlocks,
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\* Network state (good/bad)
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networkState,
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\* Validator states
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validatorStates
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vars == <<currentSlot, blocks, votes, certificates, finalizedBlocks, networkState, validatorStates>>
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(*
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Validator States:
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- active: Participating normally
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- crashed: Offline/crashed
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- byzantine: Malicious behavior
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*)
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ValidatorState == {"active", "crashed", "byzantine"}
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(*
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Network States:
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- good: Reliable communication
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- bad: Unreliable/partitions possible
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*)
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NetworkState == {"good", "bad"}
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(*
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Vote Types for Votor:
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- fast_vote: 80% stake for fast finalization
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- slow_vote: 60% stake for conservative finalization
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- skip_vote: Skip certificate for timeout
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*)
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VoteType == {"fast_vote", "slow_vote", "skip_vote"}
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(*
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Certificate Types:
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- fast_cert: Generated with 80% stake
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- slow_cert: Generated with 60% stake
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- skip_cert: Skip certificate
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*)
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CertType == {"fast_cert", "slow_cert", "skip_cert"}
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----
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\* Helper operators
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\* Calculate total stake
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TotalStake == FoldFunctionOnSet(LAMBDA x,y: x+y, 0, {StakeWeights[v] : v \in 1..NumValidators})
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\* Calculate stake for a set of validators
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StakeOf(S) == FoldFunctionOnSet(LAMBDA x,y: x+y, 0, {StakeWeights[v] : v \in S})
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\* Check if stake percentage threshold is met
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StakeThreshold(S, threshold) ==
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LET total == TotalStake
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IN (StakeOf(S) * 100) >= (total * threshold)
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\* Get honest validators (active and not byzantine)
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HonestValidators ==
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{v \in 1..NumValidators :
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validatorStates[v] = "active"}
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\* Get responsive validators (honest and network allows communication)
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ResponsiveValidators ==
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IF networkState = "good"
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THEN HonestValidators
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ELSE {v \in HonestValidators : RandomElement(1..10) > 2} \* 80% responsive in bad network
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----
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\* Initial state
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Init ==
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/\ currentSlot = 1
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/\ blocks = [s \in 1..MaxSlots |-> [v \in 1..NumValidators |-> {}]]
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/\ votes = [s \in 1..MaxSlots |-> [v \in 1..NumValidators |-> {}]]
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/\ certificates = [s \in 1..MaxSlots |-> {}]
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/\ finalizedBlocks = {}
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/\ networkState = "good"
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/\ validatorStates = [v \in 1..NumValidators |->
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CASE v \in 1..(NumValidators \div 4) -> "byzantine" \* Up to 25% Byzantine
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[] v \in (NumValidators \div 4 + 1)..(NumValidators \div 2) -> "crashed" \* Up to 25% crashed
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[] OTHER -> "active"]
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----
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\* Actions
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\* Propose a block (leader election)
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ProposeBlock ==
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/\ currentSlot <= MaxSlots
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/\ validatorStates[currentSlot % NumValidators + 1] = "active" \* Simple round-robin leader
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/\ LET leader == currentSlot % NumValidators + 1
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block == [slot |-> currentSlot, proposer |-> leader, data |-> RandomElement(1..1000)]
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IN blocks' = [blocks EXCEPT ![currentSlot][leader] = block]
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/\ UNCHANGED <<votes, certificates, finalizedBlocks, networkState, validatorStates>>
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\* Cast a vote (Votor protocol)
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CastVote ==
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/\ currentSlot <= MaxSlots
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/\ \E v \in 1..NumValidators :
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/\ validatorStates[v] = "active"
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/\ votes[currentSlot][v] = {}
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/\ LET vote_type == CASE StakeThreshold(ResponsiveValidators, 80) -> "fast_vote"
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[] StakeThreshold(ResponsiveValidators, 60) -> "slow_vote"
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[] OTHER -> "skip_vote"
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IN votes' = [votes EXCEPT ![currentSlot][v] = vote_type]
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/\ UNCHANGED <<currentSlot, blocks, certificates, finalizedBlocks, networkState, validatorStates>>
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\* Generate certificate (Votor aggregation)
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GenerateCertificate ==
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/\ currentSlot <= MaxSlots
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/\ certificates[currentSlot] = {}
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/\ LET fast_voters == {v \in 1..NumValidators :
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votes[currentSlot][v] = "fast_vote" /\ validatorStates[v] = "active"}
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slow_voters == {v \in 1..NumValidators :
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votes[currentSlot][v] = "slow_vote" /\ validatorStates[v] = "active"}
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skip_voters == {v \in 1..NumValidators :
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votes[currentSlot][v] = "skip_vote" /\ validatorStates[v] = "active"}
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IN /\ \/ /\ StakeThreshold(fast_voters, 80)
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/\ certificates' = [certificates EXCEPT ![currentSlot] = "fast_cert"]
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\/ /\ ~StakeThreshold(fast_voters, 80)
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/\ StakeThreshold(slow_voters, 60)
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/\ certificates' = [certificates EXCEPT ![currentSlot] = "slow_cert"]
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\/ /\ ~StakeThreshold(fast_voters, 80)
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/\ ~StakeThreshold(slow_voters, 60)
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/\ StakeThreshold(skip_voters, 60)
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/\ certificates' = [certificates EXCEPT ![currentSlot] = "skip_cert"]
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/\ UNCHANGED <<currentSlot, blocks, votes, finalizedBlocks, networkState, validatorStates>>
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\* Finalize block
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FinalizeBlock ==
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/\ currentSlot <= MaxSlots
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/\ certificates[currentSlot] # {}
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/\ finalizedBlocks' = finalizedBlocks \union {currentSlot}
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/\ currentSlot' = currentSlot + 1
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/\ UNCHANGED <<blocks, votes, certificates, networkState, validatorStates>>
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\* Network state changes
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NetworkFailure ==
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/\ networkState = "good"
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/\ networkState' = "bad"
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/\ UNCHANGED <<currentSlot, blocks, votes, certificates, finalizedBlocks, validatorStates>>
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NetworkRecovery ==
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/\ networkState = "bad"
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/\ networkState' = "good"
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/\ UNCHANGED <<currentSlot, blocks, votes, certificates, finalizedBlocks, validatorStates>>
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\* Validator crashes
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ValidatorCrash ==
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/\ \E v \in 1..NumValidators :
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/\ validatorStates[v] = "active"
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/\ validatorStates' = [validatorStates EXCEPT ![v] = "crashed"]
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/\ UNCHANGED <<currentSlot, blocks, votes, certificates, finalizedBlocks, networkState>>
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\* Byzantine behavior (equivocation)
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ByzantineEquivocation ==
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/\ \E v \in 1..NumValidators :
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/\ validatorStates[v] = "byzantine"
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/\ votes[currentSlot][v] # {}
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/\ votes' = [votes EXCEPT ![currentSlot][v] = "fast_vote"] \* Change vote maliciously
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/\ UNCHANGED <<currentSlot, blocks, certificates, finalizedBlocks, networkState, validatorStates>>
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----
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\* Specification
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Next ==
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\/ ProposeBlock
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\/ CastVote
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\/ GenerateCertificate
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\/ FinalizeBlock
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\/ NetworkFailure
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\/ NetworkRecovery
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\/ ValidatorCrash
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\/ ByzantineEquivocation
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Fairness ==
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/\ WF_vars(ProposeBlock)
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/\ WF_vars(CastVote)
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/\ WF_vars(GenerateCertificate)
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/\ WF_vars(FinalizeBlock)
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Spec == Init /\ [][Next]_vars /\ Fairness
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----
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\* Safety Properties
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\* No two conflicting blocks can be finalized in the same slot
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Safety_NoConflictingBlocks ==
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\A s1,s2 \in finalizedBlocks :
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s1 # s2 => blocks[s1] # blocks[s2]
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\* Certificate uniqueness - no slot has multiple certificates
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Safety_CertificateUniqueness ==
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\A s \in 1..MaxSlots :
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certificates[s] # {} => \A t \in 1..MaxSlots :
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t # s => certificates[t] # certificates[s]
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\* Chain consistency under Byzantine conditions
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Safety_ChainConsistency ==
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\A s1,s2 \in finalizedBlocks :
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s1 < s2 => blocks[s1] # blocks[s2] \* No fork
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----
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\* Liveness Properties
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\* Progress guarantee under partial synchrony with >60% honest participation
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Liveness_Progress ==
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<>[](currentSlot > MaxSlots \/ StakeThreshold(HonestValidators, 60))
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\* Fast path completion in one round with >80% responsive stake
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Liveness_FastPath ==
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\A s \in 1..MaxSlots :
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certificates[s] = "fast_cert" => StakeThreshold(ResponsiveValidators, 80)
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\* Bounded finalization time
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Liveness_BoundedFinalization ==
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\A s \in 1..MaxSlots :
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s \in finalizedBlocks => certificates[s] \in {"fast_cert", "slow_cert"}
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----
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\* Resilience Properties
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\* Safety maintained with ≤20% Byzantine stake
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Resilience_ByzantineSafety ==
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StakeOf({v \in 1..NumValidators : validatorStates[v] = "byzantine"}) <= (TotalStake * 20) \div 100
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=> Safety_NoConflictingBlocks
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\* Liveness maintained with ≤20% non-responsive stake
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Resilience_NonResponsiveLiveness ==
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StakeOf({v \in 1..NumValidators : validatorStates[v] \in {"crashed", "byzantine"}}) <= (TotalStake * 20) \div 100
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=> Liveness_Progress
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\* Network partition recovery
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Resilience_PartitionRecovery ==
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networkState = "bad" ~> networkState = "good"
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====

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