Neuro-Symbolic Integration of Hopfield Neural Network for Optimal Maximum Random kSatisfiability (Maxrksat) Representation

Boolean satisfiability logical representation is a programming paradigm that has its foundations in mathematical logic. It has been classified as an NP-complete problem that difficult practical combinatorial optimization and search problems can be easily converted into it. Random Maximum kSatisfiability (MAX-RkSAT) composed of the most consistent mapping in a Boolean formula that generates a maximum number of random satisfied clauses. Many optimization and search problems can be easily expressed by mapping the problem into a Hopfield neural network (HNN) to minimize the optimal configuration of the corresponding Lyapunov energy function. In this paper, a hybrid computational model hs been proposed that incorporates the Random Maximum kSatisfiability (MAX-RkSAT) into the Hopfield neural network (HNN) for optimal Random Maximum kSatisfiability representation (HNN-MAX-RkSAT). Hopfield neural network learning will be integrated with the random maximum satisfiability to enhance the correct neural state of the network model representation. The computer simulation using C++ has been used to demonstrate the ability of MAX-RkSAT to be embedded optimally in Hopfield neural network to serve as Neuro-symbolic integration. The performance of the proposed hybrid HNN-MAXRkSAT model has been explored and compared with the existing model. The proposed HNN-MAXRkSAT demonstrates good agreement with the existing models measured in terms of Global minimum Ratio (Gm), Hamming Distance (HD), Mean Absolute Error (MAE) and network computation Time CPU time). The proposed framework explored that MAX-RkSAT can be optimally represented in HNN and subsequently provides an additional platform for neural-symbolic integration, representing the various types of satisfiability logic.