On the complexity of the "most general" undirected firing squad synchronization problem
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
On the complexity of the “most general” firing squad synchronization problem
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
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We show that if a minimal-time solution to a fundamental distributed computation primitive, synchronizing a network path of finite-state processors, exists on the three-dimensional, undirected grid, then we can conclude the purely complexity-theoretic result $P = NP$. Every previous result on network synchronization for various network topologies either demonstrates the existence of fast synchronization solutions or proves that a synchronization solution cannot exist at all. To date, it is unknown whether there is a network topology for which there exists a synchronization solution but for which no minimal-time synchronization solution exists. Under the assumption that $P \neq NP$, this paper solves this longstanding open problem in the affirmative.