Distributed Computing

, Volume 24, Issue 6, pp 299-321

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Consensus in the presence of mortal Byzantine faulty processes

  • Josef WidderAffiliated withFormal Methods in Systems Engineering Group E184/4, Technische Universität wien Email author 
  • , Martin BielyAffiliated withEcole polytechnique Fédérale de Lausanne (EPFL)
  • , Günther GridlingAffiliated withEmbedded Computing Systems Group E182/2, Technische Universität wien
  • , Bettina WeissAffiliated withEmbedded Computing Systems Group E182/2, Technische Universität wien
  • , Jean-Paul BlanquartAffiliated withAstrium Satellites


We consider the problem of reaching agreement in distributed systems in which some processes may deviate from their prescribed behavior before they eventually crash. We call this failure model “mortal Byzantine”. After discussing some application examples where this model is justified, we provide matching upper and lower bounds on the number of faulty processes, and on the required number of rounds in synchronous systems. We then continue our study by varying different system parameters. On the one hand, we consider the failure model under weaker timing assumptions, namely for partially synchronous systems and asynchronous systems with unreliable failure detectors. On the other hand, we vary the failure model in that we limit the occurrences of faulty steps that actually lead to a crash in synchronous systems.


Consensus Byzantine fault Distributed algorithm Fault tolerance Complexity