Optimization hardness as transient chaos: revisiting a classic Nature Physics k-SAT paper

wgilpin0 · x · 2026-09-24

A thread revisits dynamical-systems approaches to combinatorial optimization: mid-1990s to 2005 work framed problems like TSP and channel assignment as Hopfield networks minimizing energy.

The core citation is Ercsey-Ravasz & Toroczkai's 2011 Nature Physics paper mapping k-SAT to a deterministic continuous-time dynamical system: beyond a constraint-density threshold, trajectories become transiently chaotic and solution-basin boundaries turn fractal, signaling hardness—yet the system still finds solutions in polynomial time even in frozen 3-SAT regimes.

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