Possibility and impossibility results in a shared memory environment

Abstract

We focus on unreliable asynchronous shared memory model which support only atomic read and write operations. For such a model we provide a necessary condition for the solvability of problems in the precence of multiple undetectable crash failures. Also, by using game-theoretical notions, a necessary and sufficient condition is provided, for the solvability of problems in the precence of multiple undetectable initial failures

Our results imply that many problems such as consensus, choosing a leader, ranking, matching and sorting are unsolvable in the presence of a single crash failure, and that variants of these problems are solvable in the presence of t − 1 crash failures but not in the presence of t crash failures.

We show that a shared memory model simulate various message passing models, and hence our impossibility results hold also for those message passing models. Our results extend and generalize known impossibility results for various asynchronous models.

Supported in part by the National Science Foundation under grant CCR-8405478, by the Hebrew Technical Institute scholarship, and by the Guttwirth Fellowship.

Supported in part by Technion V.P.R. Funds — Wellner Research Fund, and by the Foundation for Research in Electronics, Computers and Communications, administrated by the Israel Academy of Sciences and Humanities.