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Chaotic Cellular Neural/Nonlinear Networks for Solving Constraint Satisfaction


"Constraint satisfaction problems (such as Boolean satisfiability) constitute one of the hardest classes of optimization problems with many applications in technology and industry. In a recent paper the Fellow revealed a novel connection between these problems and chaotic dynamical systems. The paper provided an exact mapping of Boolean satisfiability (k-SAT) into a deterministic continuous-time dynamical system with a unique correspondence between its set of attractors and the k-SAT solutions. It was shown that optimization hardness is fundamentally equivalent to the phenomenon of chaos and turbulence: after a critical constraint density is reached, the trajectories become transiently chaotic before finding the solutions, signaling the appearance of optimization hardness. Numerical results have also shown that the presented dynamical system is very efficient in solving SAT problems. The system presented has the simplest possible form designed for fulfilling the mathematical requirements and is not yet suitable for direct implementation. However, the system is not necessarily unique. Using the same principles the goal of this project is to develop a deterministic continuous-time Cellular Neural/Nonlinear Network (CNN) model for solving constraint satisfaction. CNN models were already implemented in analog computers so this could result in a possible physical implementation of the model in the future, leading to numerous applications. The project will follow three major steps: 1) developing the CNN model and analyzing its mathematical properties. 2) Studying the efficiency of the CNN solver and properties of the transient chaotic behavior in hard problems. 3) Testing the robustness of the model to noise effects."

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EU contribution
€ 128 555,40
400084 Cluj Napoca

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Macroregiunea Unu Nord-Vest Cluj
Activity type
Higher or Secondary Education Establishments
Administrative Contact
Zoltan Neda (Prof.)
Total cost
No data