Practical SMR-style TLA+ Specification of the MultiPaxos Protocol

19 Feb 2024 - Guanzhou Hu

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The attached files present a practical TLA+ specification of MultiPaxos that very closely models how a real state machine replication (SMR) system would implement this protocol. I did not find anything similar on the web, so I’d like to share it with anyone interested.

Files of This TLA+ Spec

Below are the files composing the checkable model (organized in VSCode extension style):

• MultiPaxos.tla (main protocol spec written in PlusCal and with translation attached)
• MultiPaxos_MC.tla (entrance of running model checking; contains the checked constraints)
• MultiPaxos_MC.cfg (recommended model inputs and configurations, which should give 100% coverage of all interesting cases)
• MultiPaxos_MC_small.cfg (smaller input with one fewer write and no CommitNotice messages)

What’s Good About This Spec

This spec is different from traditional, general descriptions of Paxos/MultiPaxos in the following aspects:

• It models MultiPaxos in a practical SMR system style that’s much closer to real implementations than its traditional, abstract specs (e.g., this)
  • All servers explicitly replicate a log of instances, each holding a command
  • Numbers of client write/read commands are made model inputs
  • Explicit termination condition is defined, thus semi-liveness can be checked by not having deadlocks
  • Safety constraint is defined as a clean client-viewed linearizability property upon termination
  • Replica node failure is injected to assure the protocol’s fault-tolerance level
  • See the detailed comments in the source files…
• Careful optimizations are applied to the spec to reduce the state space W.L.O.G.
  • Model checking with recommended inputs completes in < 22 min on a 40-core server machine
  • Commenting out the HandleCommitNotice action (which is the least significant) and having one fewer request reduces check time down to < 10 secs
• It is easy to extend this spec and add even more practical features
  • Leader lease and local read
  • Asymmetric write/read quorum sizes
  • …

This spec has been accepted into the official TLA+ Examples repo! ¹

Here are some links I found particularly useful when developing this spec by myself: ^{2 3 4 5}

Update: Extended Spec with Extra Features

Below are the files composing an extended version of the spec along with model inputs:

• MultiPaxos.tla (extended main protocol spec written in PlusCal and with translation attached)
• MultiPaxos_MC.tla (entrance of running model checking; contains the checked constraints)
• MultiPaxos_MC.cfg (recommended model inputs and configurations, which should give 100% coverage of all interesting cases with default features)
• MultiPaxos_MC_small.cfg (smallest input for sanity check)
• MultiPaxos_MC_rwqrm.cfg (input demonstrating asymmetric write/read quorum sizes)
• MultiPaxos_MC_lease.cfg (input demonstrating stable leader leases and local read)

What’s New in the Extended Spec

The extended spec includes the following extra features/variants of MultiPaxos that are very essential and useful in practice:

• Only keep writes in the log (while reads squeeze in between writes)
• Asymmetric write/read quorum sizes
• Stable leader lease and local read at leader

References

1. https://github.com/tlaplus/Examples ↩

2. https://lamport.azurewebsites.net/tla/tutorial/home.html ↩

3. https://learntla.com/index.html ↩

4. https://lamport.azurewebsites.net/tla/summary-standalone.pdf ↩

5. https://tla.msr-inria.inria.fr/tlatoolbox/doc/model/distributed-mode.html ↩

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