BRAN2SAT: Redundant satisfiability logic in Lyapunov-based discrete Hopfield neural network

Abstract This study introduces a novel non-systematic logical structure, termed B-type Random 2-Satisfiability, which incorporates non-redundant first- and second-order clauses, as well as redundant second-order clauses. The proposed logical rule is implemented in the discrete Hopfield neural network using the Wan Abdullah method, with the corresponding cost function minimized through an exhaustive search algorithm to reduce the inconsistency of the logical rules. The inclusion of redundant literals is intended to enhance the capacity of the model to extract overlapping knowledge. Additionally, the performance of B-type Random 2-Satisfiability with varying clause proportions in the discrete Hopfield neural network is evaluated using various metrics, including learning error, retrieval error, weight error, energy analysis, and similarity analysis. Experimental results indicate that the model demonstrates superior efficiency in synaptic weight management and offers a broader solution space when the number of the three types of clauses is selected randomly.