2021/09/03 by Hugo Rincon Galeana, Galeana, Hugo Rincon, Sergio Rajsbaum +3
Computer Science · #Algebraic Topology (math.AT) #Computability, Logic, AI Algorithms #Distributed #Distributed systems and fault tolerance #FOS: Computer and information sciences #FOS: Mathematics #Logic, programming, and type systems #Parallel #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.2109.01439
openalex publication_date 2021/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The celebrated 1999 Asynchronous Computability Theorem (ACT) of Herlihy and Shavit characterized the distributed tasks that are wait-free solvable, and thus uncovered a deep connection with algebraic topology. We present a novel interpretation of this theorem, through the notion of continuous task, defined by an input/output specification that is a continuous function. To do so, we introduce a chromatic version of a foundational result for algebraic topology: the simplicial approximation theorem. In addition to providing a different proof of the ACT, the notion of continuous task seems interesting in itself. Indeed, besides the fact that certain distributed problems are naturally specified by continuous functions, continuous tasks have an expressive power that also allows to specify the density of desired outputs for each combination of possible inputs,for example.