Consensus with dual failure modes

The problem of achieving consensus in a distributed system is discussed. Systems are treated in which either or both of two types of faults may occur: dormant (essentially omission and timing faults) and arbitrary (exhibiting arbitrary behavior, commonly referred to as Byzantine). Previous results showed that are number of dormant faults may be tolerated when there are no arbitrary faults and that, at most, [n-1/3] arbitrary faults may be tolerated when there are no dormant faults (n is the number of processors). A continuum is established between the previous results: an algorithm exists iff n >f_max+2m_max and c >f_max+m_max (where c is the system connectivity), when faults are constrained so that there are at most f_max and at most m_max of these that are arbitrary. An algorithm is given and compared to known algorithms. A method is given to establish virtual links so that the communications graph appears completely connected