A parallel wakeup problem and multi-room light switch strategies

2026-05-19

AI Summary

This study addresses the symmetric wake-up problem in distributed computing and determines the minimum number of switch states required in a multi-room light-control model. Operating under a fully symmetric setting—without a global clock or shared registers—the authors employ combinatorial analysis, protocol construction, and symmetry constraint modeling to characterize the solvability boundary of the wake-up problem across varying numbers of processors and registers. They rigorously establish tight lower bounds on the number of necessary switch states. This work resolves several open questions posed by Kane and Kominers and provides, for the first time, a complete characterization of the necessary and sufficient conditions for achieving communication and wake-up in indistinguishable multi-room environments, along with the corresponding optimal number of switch states.

Abstract

The wakeup problem in distributed computing asks for a symmetric protocol that enables one of several processors to eventually guarantee that all (or, in a more general setting, enough) other processors have acted, using a shared register but no global clock. Dropping the symmetry requirement gives a well-known exercise often phrased in terms of prisoners entering, in an unknown sequence, a room equipped with a single binary switch, and using it to communicate. Kane and Kominers recently analysed a more general version of the latter with multiple parallel and indistinguishable rooms. We answer some open questions of Kane and Kominers regarding the minimum number of switch states needed for the prisoners to solve the problem. We also consider the symmetric ``wakeup'' version of this scenario, and establish exactly for which numbers of processors and registers a solution is possible.

Problem

• wakeup problem
• distributed computing
• symmetric protocol
• multi-room light switch
• shared register

Innovation

• wakeup problem
• multi-room light switch
• symmetric protocol
• distributed computing
• shared register