On the Hardness of the Strongly Dependent Decision Problem

Abstract

We present necessary and sufficient conditions for solving the strongly dependent decision (SDD) problem in various distributed systems. Our main contribution is a novel characterization of the SDD problem based on point-set topology. For partially synchronous systems, we show that any algorithm that solves the SDD problem induces a set of executions that is closed with respect to the point-set topology. We also show that the SDD problem is not solvable in the asynchronous system augmented with any arbitrarily strong failure detectors.