YRAN2SAT: : A novel flexible random satisfiability logical rule in discrete hopfield neural network

The current development of the satisfiability logical representation in Discrete Hopfield Neural Network has two prominent perspectives which are systematic and non-systematic logic. In general, systematic logic was reported to provide us with more consistent and very predictable behaviour whereas non-systematic logic provides broader solution space with a non-predictable pattern. However, the main weaknesses of the existing satisfiability logical rule are the non-flexibility of the logical composition and a low capability to represent the feature's intersection between systematic and non-systematic logic. In this paper, a flexible logical rule called Y-Type Random 2 Satisfiability was proposed by combining the structure of the systematic and non-systematic logic, as a hybrid satisfiability logical rule. The proposed logical rule enumerates randomly based on the structure of either first-order, second-order, or both orders of the clause. The proposed logical rule will be implemented into Discrete Hopfield Neural Network with the aim of minimizing the cost function. The behaviour of the proposed logical rule is compared with the existing satisfiability logic in terms of various performance evaluation metrics. The results show the improvement of the solution capacity for our proposed logic in terms of synaptic weight assessments, various error analyses, energy evaluation, the effects of different states, similarity index, and variability of states. The findings confirm that the proposed logical rule serves as a flexible symbolic instruction for the Discrete Hopfield Neural Network by obtaining the optimal synaptic weights and more variation of neuron states in solution spaces.