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• W2030586674 abstract "Boolean satisfiability [1] (k-SAT) is one of the most studied optimization problems, as an efficient (that is, polynomial-time) solution to k-SAT (for $kgeq 3$) implies efficient solutions to a large number of hard optimization problems [2,3]. Here we propose a mapping of k-SAT into a deterministic continuous-time dynamical system with a unique correspondence between its attractors and the k-SAT solution clusters. We show that beyond a constraint density threshold, the analog trajectories become transiently chaotic [4-7], and the boundaries between the basins of attraction [8] of the solution clusters become fractal [7-9], signaling the appearance of optimization hardness [10]. Analytical arguments and simulations indicate that the system always finds solutions for satisfiable formulae even in the frozen regimes of random 3-SAT [11] and of locked occupation problems [12] (considered among the hardest algorithmic benchmarks); a property partly due to the system's hyperbolic [4,13] character. The system finds solutions in polynomial continuous-time, however, at the expense of exponential fluctuations in its energy function." @default.
• W2030586674 created "2016-06-24" @default.
• W2030586674 creator A5038398506 @default.
• W2030586674 creator A5091671977 @default.
• W2030586674 date "2011-10-02" @default.
• W2030586674 modified "2023-10-06" @default.
• W2030586674 title "Optimization hardness as transient chaos in an analog approach to constraint satisfaction" @default.
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• W2030586674 doi "https://doi.org/10.1038/nphys2105" @default.
• W2030586674 hasPublicationYear "2011" @default.
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