1 Quorum System

1.5 Process failures
Following are the usual kind of failures that typically occur by object/process in both shared
memory and message-passing systems.
Definition 6 If a process behaves correctly according to its protocol, then it’s correct. A
crash failure is one where the process (or shared object) stops executing protocol permanently.
A process is benign if it’s correct or it has a crash failure. A process that is not benign is
called Byzantine or malicious.
Byzantine failures are the worst kind of failures. They can be again of two types:
1. Unauthenticated: Here, a process can pretend to be some other process and can possibly
forge signature of others. Processes can send arbitrary messages in message passing
model or invoke arbitrary operations in shared memory model.
2. Authenticated: We assume digital signature of each process in this type of failure of
Byzantine failure and thus no process can forge other process’s signature.
Definition 7 A fault configuration is a vector C ∈ {0, 1} n such that C i = 1 if and only if
the process s i has failed.
Definition 8 Given a set of processes S and an execution e, we define alive(e, S) as the set
of correct processes in S, and faulty(e, S) as the set of faulty processes in S.
We’ll write them as alive(S) and faulty(S), when e is clear from the context.
Definition 9 A set of processes Q ⊆ S is available if Q ⊆ alive(S).
We also consider probabilistic fault-tolerant model, where each process s i in the set S fails
independently with probability p i .
Definition 10 If p i = p for all i, then it’s called a uniform probabilistic fault tolerant model.
References
[Thomas, 1979] Thomas, R. H. (1979). A majority consensus approach to concurrency control
for multiple copy databases. ACM Trans. Database Syst., 4(2):180–209.
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