Developing a Consensus Algorithm Using Stepwise Refinement
Consensus problems arise in any area of computing where distributed processes must come to a joint decision. Although solutions to consensus problems have similar aims, they vary according to the processor faults and network properties that must be taken into account, and modifying these assumptions will lead to different algorithms. Reasoning about consensus protocols is subtle, and correctness proofs are often informal. This paper gives a fully formal development and proof of a known consensus algorithm using the stepwise refinement method Event-B. This allows us to manage the complexity of the proof process by factoring the proof of correctness into a number of refinement steps, and to carry out the proof task concurrently with the development. During the development the processor faults and network properties on which the development steps rely are identified. The research outlined here is motivated by the observation that making different choices at these points may lead to alternative algorithms and proofs, leading to a refinement tree of algorithms with partially shared proofs.
KeywordsConsensus Algorithms Stepwise Refinement Verification Event-B
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- 5.Charron-Bost, B., Merz, S.: Formal Verification of a Consensus Algorithm in the Heard-Of Model. Int. J. Software and Informatics 3(2-3), 273–303 (2009)Google Scholar
- 8.Krenický, R., Ulbrich, M.: Deductive verification of a byzantine agreement protocol. Technical report, Karlsruhe Institute of Technology (April 2010)Google Scholar
- 12.Lynch, N.A.: Distributed Algorithms, 1st edn. Morgan Kaufmann, San Francisco (1997)Google Scholar
- 13.Sprenger, C., Basin, D.: Developing security protocols by refinement. In: 17th ACM Conference on Computer and Communications Security, CCS 2010 (2010)Google Scholar
- 14.Truong, N.-T., Trinh, T.-B., Nguyen, V.-H.: Coordinated consensus analysis of multi-agent systems using Event-B. In: Seventh IEEE International Conference on Software Engineering and Formal Methods, pp. 201–209 (2009)Google Scholar