This paper introduces a new approach to enhance performance in performing logic programming in the Hopfield neural network by using agent-based modeling. Hopfield networks have been broadly utilized to solve problems of combinatorial optimization. However, this network yielded a satisfiability problem because the network has grown larger, and it is more complex. Therefore, an improved algorithm has been proposed to enhance the Hopfield network’s capability by using the technique of fuzzy logic to provide more efficient energy relaxation and to avoid the local minimum solutions. Agent-based modeling has been introduced in this paper to conduct computer simulations, which aim at verifying and validating the introduced approach. By applying the technique of fuzzy Hopfield neural network clustering in the system, better quality solutions are produced, and the network is handled better despite the increasing complexity. Also, the solutions converged faster by the system. Accordingly, this technique of the fuzzy Hopfield neural network clustering in the system has produced better-quality solutions.

The artificial neural network system's dynamical behaviors are greatly dependent on the construction of the network. Artificial Neural Network's outputs suffered from a shortage of interpretability and variation lead to severely limited the practical usability of artificial neural networks for doing the logical program. The goal for implementing a logical program in Hopfield neural network rotates rounding minimizing the energy function of the network to reaching the best global solution which ordinarily fetches local minimum solution also. Nevertheless, this problem can be overcome by utilizing the hyperbolic tangent activation function and the Boltzmann Machine in the Hopfield neural network. The foremost purpose of this article is to explore the solution quality obtained from the Hopfield neural network to solve 2 Satisfiability logic (2SAT) by using the Mean-Field Theory algorithm. We want for replacing the real unstable prompt local field for the separate neurons into the network by its average local field utility. By using the solution to the deterministic Mean-Field Theory (MFT) equation, the system will derive the training algorithms in which time-consuming stochastic measures of collections are rearranged. By evaluating the outputs of global minima ratio (zM), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) with computer processing unit (CPU) time as benchmarks, we find that the MFT theory successfully captures the best global solutions by relaxation effects energy function.

Bezier curve is one of the most pragmatic curves that has vast application in computer aided geometry design. Unlike other normal curves, any Bezier curve model must follow the properties of Bezier curve. In our paper, we proposed the reconstruction of Bezier models by implementing satisfiability problem in Hopfield neural network as Bezier properties verification technique. We represent our logic construction to 2-satisfiability (2SAT) clauses in order to represent the properties of the Bezier curve model. The developed Bezier model will be integrated with Hopfield neural network in order to detect the existence of any non-Bezier curve. Microsoft Visual C++ 2013 is used as a platform for training, testing and validating of our proposed design. Hence, the performance of our proposed technique is evaluated based on global Bezier model and computation time. It has been observed that most of the model produced by HNN-2SAT are Bezier curve models.

Highly-interconnected Hopfield network with Content Addressable Memory (CAM) are shown to be extremely effective in constraint optimization problem. The emergent of the Hopfield network has producing a prolific amount of research. Recently, 3 Satisfiability (3-SAT) has becoming a tool to represent a variety combinatorial problems. Incorporated with 3-SAT, Hopfield neural network (HNN-3SAT) can be used to optimize pattern satisfiability (Pattern-SAT) problem. Hence, we proposed the HNN-3SAT with Hyperbolic Tangent activation function and the conventional McCulloch-Pitts function. The aim of this study is to investigate the accuracy of the pattern generated by our proposed algorithms. Microsoft Visual C++ 2013 is used as a platform for training, testing and validating our Pattern-SAT design. The detailed performance of HNN-3SAT of our proposed algorithms in doing Pattern-SAT will be discussed based on global pattern-SAT and running time. The result obtained from the simulation demonstrate the effectiveness of HNN-3SAT in doing Pattern-SAT.

This paper presents the technique for accelerating 3-Satisfiability (3-SAT) logic programming in Hopfield neural network. The core impetus for this work is to integrate activation function for doing 3-SAT logic programming in Hopfield neural network as a single hybrid network. In logic programming, the activation function can be used as a dynamic post optimization paradigm to transform the activation level of a unit (neuron) into an output signal. In this paper, we proposed Hyperbolic tangent activation function and Elliot symmetric activation function. Next, we compare the performance of proposed activation functions with a conventional function, namely McCulloch-Pitts function. In this study, we evaluate the performances between these functions through computer simulations. Microsoft Visual C++ 2013 was used as a platform for training, validating and testing of the network. We restrict our analysis to 3-Satisfiability (3-SAT) clauses. Moreover, evaluations are made between these activation functions to see the robustness via aspects of global solutions, global Hamming distance, and CPU time.

Very large scale integration (VLSI) circuit comprises of integrated circuit (IC) with transistors in a single chip, widely used in many sophisticated electronic devices. In our paper, we proposed VLSI circuit design by implementing satisfiability problem in Hopfield neural network as circuit verification technique. We restrict our logic construction to 2-Satisfiability (2-SAT) and 3-Satisfiability (3-SAT) clauses in order to suit with the transistor configuration in VLSI circuit. In addition, we developed VLSI circuit based on Hopfield neural network in order to detect any possible error earlier than the manual circuit design. Microsoft Visual C++ 2013 is used as a platform for training, testing and validating of our proposed design. Hence, the performance of our proposed technique evaluated based on global VLSI configuration, circuit accuracy and the runtime. It has been observed that the VLSI circuits (HNN-2SAT and HNN-3SAT circuit) developed by proposed design are better than the conventional circuit due to the early error detection in our circuit.

In this study, linear and nonlinear methods were used to model forecasting performances on the daily crude oil production data of the Nigerian National Petroleum Corporation (NNPC). The linear model considered here is the random walk with drift, while the nonlinear model is the feed forward neural network model. The results indicate that nonlinear methods have better forecasting performance greater than linear methods based on the mean error square sense. The root mean square error (RMSE) and the mean absolute error (MAE) were applied to ascertain the assertion that nonlinear methods have better forecasting performance greater than linear methods. Autocorrelation functions emerging from the increment series, that is, log difference series and difference series of the daily crude oil production data of the NNPC indicates significant autocorrelations. As a result of the foregoing assertion we deduced that the daily crude oil production series of the NNPC is not firmly a random walk process. However, the original daily crude oil production series of the NNPC was considered to be a random walk with drift when we are not trying to forecast immediate values. The analysis for this study was simulated using MATLAB software, version 8.03.