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At PODC 2014, A. Most\'efaoui, H. Moumen, and M. Raynal presented a new andsimple randomized signature-free binary consensus algorithm (denoted here MMR)that copes with the net effect of asynchrony Byzantine behaviors. Assumingmessage scheduling is fair and independent from random numbers MMR is optimalin several respects: it deals with up to t Byzantine processes where t < n/3and n is the number of processes, O(n\^2) messages and O(1) expected time. Thepresent article presents a non-trivial extension of MMR to an even morefault-prone context, namely, in addition to Byzantine processes, it considersalso that the system can experience transient failures. To this end itconsiders self-stabilization techniques to cope with communication failures andarbitrary transient faults (such faults represent any violation of theassumptions according to which the system was designed to operate).  The proposed algorithm is the first loosely-self-stabilizing Byzantinefault-tolerant binary consensus algorithm suited to asynchronousmessage-passing systems. This is achieved via an instructive transformation ofMMR to a self-stabilizing solution that can violate safety requirements withprobability Pr= O(1/(2\^M)), where M is a predefined constant that can be setto any positive integer at the cost of 3 M n + log M bits of local memory. Inaddition to making MMR resilient to transient faults, the obtainedself-stabilizing algorithm preserves its properties of optimal resilience andtermination, (i.e., t < n/3, and O(1) expected time). Furthermore, it onlyrequires a bounded amount of memory.

Loosely-self-stabilizing Byzantine-tolerant Binary Consensus for Signature-free Message-passing Systems