The fault span of crash failures

Abstract

Abstract. A crashing network protocol is an asynchronous protocol whose memory does not survive crashes. We show that a crashing network protocol that works over unreliable links can be driven to arbitrary global states, where each node is in a state reached in some (possibly different) execution, and each link has an arbitrary mixture of packets sent in (possibly different) executions. Our theorem considerably generalizes an earlier result, due to Fekete et al., which states that there is no correct crashing Data Link Protocol. For example, we prove that there is no correct crashing protocol for token passing and for many other resource allocation protocols such as k-exclusion, and the drinking and dining philosophers problems. We further characterize the reachable states caused by crash failures using reliable non-FIFO and reliable FIFO links. We show that with reliable non-FIFO links any acyclic subset of nodes and links can be driven to arbitrary states. We show that with reliable FIFO links, only nodes can be driven to arbitrary states. Overall, we show a strict hierarchy in terms of the set of states reachable by crash failures in the three link models.

Fast and Compact Distributed Verification and Self-stabilization of a DFS Tree

“…Self-stabilization deals with the faults that entail an arbitrary corruption of the state of a system. These faults are rather severe in nature but do not occur very frequently in reality [31]. Table 1.1 summarizes the known complexity results for self-stabilizing DFS algorithms.…”

Self-Stabilizing Algorithms

“…Self-stabilization would seem to be related more to the concept of convergence in mathematics or control theory, where the objective is to reach a fixed point regardless of the initial position; the fixed point corresponds here to an appropriate execution. Being capable of starting with an arbitrary state may seem odd (since it would seem that the initial states of the elements are always well known), but studies [73] have shown that if a distributed system is subjected to stopping and restarting-type node failures (which correspond to a definite failure followed by a reinitialization), and communications cannot be totally reliable (some communications may be lost, duplicated or, desequenced), then an arbitrary state of the system can actually be achieved. Even if the probability of the execution that leads to this arbitrary state is negligible in normal conditions, it is not impossible for an attack on the system to attempt to reproduce such an execution.…”

Rigorous Performance Evaluation of Self-Stabilization Using Probabilistic Model Checking

“…When the system is hit by faults and driven to some arbitrary state [24], it is guaranteed to recover proper behavior within a finite number of execution steps. Once the system reaches such good behavior, typically specified by a set of legitimate states, it remains in this set thereafter in the absence of new faults.…”