Brief Announcement: A Sheaf-Theoretic Characterization of Tasks in Distributed Systems

Abstract

Task solvability lies at the heart of distributed computing, with direct implications for both theoretical understanding and practical system design. A fundamental challenge in distributed computing is constructing global solutions from local computations and information. Sheaf theory addresses this challenge by providing a mathematical framework for assessing globally consistent properties from locally defined data. In this paper, we introduce a sheaf-theoretic characterization of task solvability by defining the novel construction of a task sheaf, whose sections correspond to valid solutions of a task. Furthermore, we show that the cohomology of a task sheaf may be used to compute solving protocols, thus establishing a connection between distributed computing and sheaf theory for both protocol design and impossibility analysis.