A Rigorous Correctness Proof for Pastry

Noran Azmy (1, 2) , Stephan Merz (3, 1, 4) , Christoph Weidenbach (1, 2)

1 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
2 MPII - Max-Planck-Institut für Informatik
3 MOSEL - Proof-oriented development of computer-based systems
4 MSR - INRIA - Microsoft Research - Inria Joint Centre

Peer-to-peer protocols for maintaining distributed hash tables, such as Pastry or Chord, have become popular for a class of Internet applications. While such protocols promise certain properties concerning correctness and performance, verification attempts using formal methods invariably discover border cases that violate some of those guarantees. Tianxiang Lu reported correctness problems in published versions of Pastry and also developed a model, which he called LuPastry, for which he provided a partial proof of correct delivery assuming no node departures, mechanized in the TLA+ Proof System. Lu's proof is based on certain assumptions that were left unproven. We found counterexamples to several of these assumptions. In this paper, we present a revised model and rigorous proof of correct delivery, which we call LuPastry+. Aside from being the first complete proof, LuPastry+ also improves upon Lu's work by reformulating parts of the specification in such a way that the reasoning complexity is confined to a small part of the proof.

Domaines: Logique en informatique [cs.LO]

Noran Azmy, Stephan Merz, Christoph Weidenbach. A Rigorous Correctness Proof for Pastry. Abstract State Machines, Alloy, B, TLA, VDM, and Z - 5th International Conference, ABZ 2016, 2016, Linz, Austria. pp.86-101, ⟨10.1007/978-3-319-33600-8_5⟩. ⟨hal-01322342⟩