J-type random 2, 3 satisfiability a higher-order logical rule in discrete hopfield neural network

The Discrete Hopfield Neural Network has been widely used for solving combinatorial optimization problems. DHNN is a simple structure with no hidden layer and binary input/output which leads to lower complexity compared to other networks. Satisfiability as a neuron representation is considered a suitable logical structure due to its simple construction. DHNN model has the potential for enhancement by incorporating various logical rules. The main problem of existing work is the need for higher-order logical rules combined with systematic, non-systematic logic. This paper proposed a novel satisfiability logical structure named J-Type Random 2,3 Satisfiability by considering both the characteristics of the second and third-order variable per clause. The proposed logical rule randomly assigns values based on the structure of either second-order, third-order, or both orders of the clause. The proposed J Random 2,3 Satisfiability logical rule will store the information externally and only be true if all the clauses are satisfiable. This logic will be implemented into the Discrete Hopfield Neural Network. By utilizing the proposed hybrid logical rule, specifically the J Random 2,3 Satisfiability, the neuron in the Hopfield Neural Network can be effectively modeled. The model will be evaluated using various performance metrics in terms of learning error, retrieval error, energy analysis, and similarity analysis. The proposed logic will undergo a comparison analysis with previously established logical rules. Based on the ratio of global solutions, the proposed model exhibited a slower decline from 1 to 0 as the number of neurons increased which suggests that the proposed model will outperform existing models in retrieving global neuron state.

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