Haslegrave et al. solve multi-room light switch wakeup problem

In a new arXiv paper (2605.19488), John Haslegrave, Paul A. Russell, and Mark Walters tackle a classic distributed computing puzzle: the parallel wakeup problem. The scenario involves prisoners entering rooms with binary switches in unknown order, using them to communicate. Kane and Kominers previously extended this to multiple parallel and indistinguishable rooms, leaving open questions about minimum switch states and symmetric wakeup feasibility. The new work answers those questions, providing exact bounds on the number of switch states required for a deterministic solution. It also explores the symmetric 'wakeup' variant where any processor can initiate the protocol, establishing precise conditions for solvability based on the numbers of processors and shared registers.

The research has implications for distributed systems lacking global clocks, where symmetric protocols must ensure all processors eventually act. By quantifying the minimal communication overhead (switch states) needed, the results help design more efficient consensus or coordination algorithms. The paper bridges combinatorics, discrete mathematics, and distributed computing, offering theoretical grounding for practical protocol design. While not directly AI-related, the findings could influence parallel algorithms used in AI training or multi-agent coordination. The 13-page paper is available for review on arXiv and is pending DOI registration.