Abstract

A snapshot shared memory algorithm is presented, allowing a set off+1processes, anyfof which may exhibit stopping failures, to “simulate ” a larger numbernof processes, also with at mostffailures. One application of this simulation algorithm is to convert an arbitraryk-fault-tolerantn-process solution for thek-set-agreement problem into a wait-freek+1-process solution for the same problem. Since thek+1-process k-set-agreement problem has been shown to have no wait-free solution [4, 16, 24], this transformation implies that there is nok-fault-tolerant solution to then-processk-set-agreement problem, for anyn. More generally, the algorithm satisfies the requirements of a fault-tolerant distributed simulation. The distributed simulation implements a notion of fault-tolerant reducibility between decision problems. These notions are defined, and examples of their use are provided. The algorithm is presented and verified in terms of I/O automata. The presentation has a great deal of interesting modularity, expressed by I/O automaton composition and both forward and backward simulation relations. Composition is used to include a safe agreement module as a subroutine. Forward and backward simulation relations are used to view the algorithm as implementing a multi-try snapshot strategy. The main algorithm works in snapshot shared memory systems; a simple modification of the algorithm that works in read/write shared memory systems is also presented.

Citations