A generalized asynchronous computability theorem

TL;DR

This paper generalizes the asynchronous computability theorem by providing topological conditions for task solvability in various distributed models, simplifying the analysis of complex resilient tasks.

Contribution

It introduces a topological framework that extends the classical ACT to broader models, enabling easier verification of task solvability.

Findings

Reformulation of task solvability using topological conditions.

Application to a complex $t$-resilient task demonstrating simplified analysis.

Confirmation of $t$-resilient solvability through the generalized theorem.

Abstract

We consider the models of distributed computation defined as subsets of the runs of the iterated immediate snapshot model. Given a task $T$ and a model $M$, we provide topological conditions for $T$ to be solvable in $M$. When applied to the wait-free model, our conditions result in the celebrated Asynchronous Computability Theorem (ACT) of Herlihy and Shavit. To demonstrate the utility of our characterization, we consider a task that has been shown earlier to admit only a very complex $t$-resilient solution. In contrast, our generalized computability theorem confirms its $t$-resilient solvability in a straightforward manner.