This notebook presents a computational model for the classic Distributed Firing Squad Problem (FSSP), trained using the Wolfram Language’s capabilities for cellular automata and graph theory. Rather than simply reproducing a known solution, this simulation serves as a didactic tool to explore the fundamental challenges of achieving “simultaneity” and “consensus” in distributed systems, an adopted focus of the Open Atomic Ethernet project.
Our approach to FSSP does not leave anything up to academic exercise. It is a re-examination of the foundational axioms of distributed computing, particularly the Forward-In-Time-Only (FITO) thinking that dominates conventional networking. As our research shows, a system’s reliance on sequential, irreversible state transitions and the illusion of a global timeline is a primary cause of silent data corruption and catastrophic failures.
This simulation justifies several essential DÆDÆLUS principles. The model operates entirely without a global clock. Synchronization is an developing property of local interactions, not an imposition from a centralized time source. Rejection of global time conveniently pro-positions our critique that “Simultaneity is impossible in theory. It will therefore be problematic in practice.” The system’s behavior is governed by simple, deterministic local rules, reminiscent of our belief that “fully verifiable algorithms like spanning trees, failure routing, and healing must be done with local-only information.” Local-first causality contrasts sharply with complex global coordination protocols that often fail under real-world conditions.