A partial equivalence between shared-memory and message-passing in an asynchronous fail-stop distributed environment

This paper presents a schematic algorithm for distributed systems. This schematic algorithm uses a “black-box” procedure for communication, the output of which must meet two requirements: a global-order requirement and a deadlock-free requirement. This algorithm is valid in any distributed system model that can provide such a communication procedure that complies with these requirements. Two such models exist in an asynchronous fail-stop environment: one in the shared-memory model and one in the message-passing model. The implementation of the block-box procedure in these models enables us to translate existing algorithms between the two models whenever these algorithms are based on the schematic algorithm. We demonstrate this idea in two ways. First, we present a randomized algorithm for the consensus problem in the message-passing model based on the algorithm of Aspnes and Herlihy [AH] in the shared-memory model. This solution is the fastest known randomized algorithm that solves the consensus problem against a strong fail-stop adversary with one-half resiliency. Second, we solve the processor renaming problem in the shared-memory model based on the solution of Attiyaet al. [ABD+] in the message-passing model. The existence of the solution to the renaming problem should be contrasted with the impossibility result for the consensus problem in the shared-memory model [CIL], [DDS], [LA].