On the Hardness of the Strongly Dependent Decision Problem

TL;DR

This paper provides a topological characterization of the strongly dependent decision problem in distributed systems, establishing conditions for solvability in different system models and showing its impossibility in certain asynchronous settings.

Contribution

It introduces a novel topological framework for analyzing the SDD problem and characterizes its solvability across various distributed system models.

Findings

SDD problem solutions correspond to closed sets in point-set topology.

No solution exists for SDD in asynchronous systems with any strong failure detectors.

The paper offers necessary and sufficient conditions for SDD solvability in different models.

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.