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The satisfiability problem (SAT) is one of the most basic and important problems in computer science. We have proposed a recurrent analog neural network called Lagrange Programming neural network with Polarized High-order connections (LPPH) for the SAT, together with a method of parallel execution of LPPH. Experimental results demonstrate a high speedup ratio. Furthermore this method is very easy to realize by hardware. LPPH dynamics has an important parameter, the attenuation coefficient, known to strongly affect LPPH execution speed, but determining a good value of attenuation coefficient is difficult. Experimental results show that the parallel execution reduces this difficulty. In this paper we propose a method to assign different values of attenuation coefficients to LPPHs used in the parallel execution. The values are generated uniformly randomly or randomly using a probability density function.

Using Attenuation Coefficient Generating Function in Parallel Execution of Neural Networks for Solving SAT