What can be computed in a distributed system?

Abstract

Not only the world is distributed, but more and more applications are distributed. Hence, a fundamental question is the following one: What can be computed in a distributed system? The answer to this question depends on the environment in which evolves the considered distributed system, i.e., on the assumptions the system relies on. This environment is very often left implicit and nearly always not formulated in terms of precise underlying requirements. In the extreme case where the environment is such that there is no synchrony assumption and the computing entities may commit failures, many problems become impossible to solve (in these cases, a network of Turing machines where some machines may crash, is less powerful than a single reliable Turing machine). Given a distributed computing problem, it is consequently important to know the weakest assumptions (lower bounds) that give the limits beyond which the considered distributed problem cannot be solved. This paper is a short introduction to this kind of issues. It first presents a few of elements related to distributed computability, and then briefly addresses distributed complexity issues. The style of the paper is voluntarily informal. © 2014 Springer-Verlag Berlin Heidelberg.