  Guerraoui proposed an indulgent solution for the binary consensus problem.
Namely, he showed that an arbitrary behavior of the failure detector never
violates safety requirements even if it compromises liveness. Consensus
implementations are often used in a repeated manner. Dutta and Guerraoui
proposed a zero-degrading solution, \ie during system runs in which the failure
detector behaves perfectly, a node failure during one consensus instance has no
impact on the performance of future instances.
  Our study, which focuses on indulgent zero-degrading binary consensus, aims
at the design of an even more robust communication abstraction. We do so
through the lenses of self-stabilization - a very strong notion of
fault-tolerance. In addition to node and communication failures,
self-stabilizing algorithms can recover after the occurrence of arbitrary
transient faults; these faults represent any violation of the assumptions
according to which the system was designed to operate (as long as the algorithm
code stays intact).
  This work proposes the first, to the best of our knowledge, self-stabilizing
algorithm for indulgent zero-degrading binary consensus for time-free
message-passing systems prone to detectable process failures. The proposed
algorithm has an O(1) stabilization time (in terms of asynchronous cycles) from
arbitrary transient faults. Since the proposed solution uses an {\Omega}
failure detector, we also present the first, to the best of our knowledge,
self-stabilizing asynchronous {\Omega} failure detector, which is a variation
on the one by Most\'efaoui, Mourgaya, and Raynal.
