Random Satisfiability: A Higher-Order Logical Approach in Discrete Hopfield Neural Network

A conventional systematic satisfiability logic suffers from a nonflexible logical structure that leads to a lack of interpretation. To resolve this problem, the advantage of introducing nonsystematic satisfiability logic is important to improve the flexibility of the logical structure. This paper proposes Random 3 Satisfiability (<italic>RAN3SAT</italic>) with three types of logical combinations (<inline-formula> <tex-math notation="LaTeX">$k = 1, 3, k =2, 3$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$k =1$ </tex-math></inline-formula>, 2, 3) to report the behaviors of multiple logical structures. The different types of <italic>RAN3SAT</italic> enforced with Discrete Hopfield Neural Network (DHNN) are included with benchmark searching techniques, such as Exhaustive Search algorithm. Additionally, to strengthen and certify the behavior of the proposed model, we extensively conducted several performance evaluation metrics with a specific number of neurons. In particular, the experimental results revealed that <italic>RAN3SAT</italic> was able to be implemented in DHNN, and each logical combination has its characteristics. Nonetheless, <italic>RAN3SAT</italic> provides more neuron variations in the whole solution space. The proposed model can also be applied in real-world applications such as the logic mining approach since <italic>RAN3SAT</italic> consists of various logic combinations that behave as input language to transform raw data into informative output.

[1]  J. J. Hopfield,et al.  “Neural” computation of decisions in optimization problems , 1985, Biological Cybernetics.

[2]  A. Ochiai.  Zoogeographical Studies on the Soleoid Fishes Found in Japan and its Neighbouring Regions-III , 1957 .

[3]  Saratha Sathasivam,et al.  Quality Solution of Logic Programming in Hopfield Neural Network , 2019 .

[4]  Morteza Esfandyari,et al.  Stock Market Index Prediction Using Artificial Neural Network , 2016 .

[5]  Mostafa Khanzadi,et al.  Billiards-inspired optimization algorithm; a new meta-heuristic method , 2020 .

[6]  Saratha Sathasivam,et al.  Enhanced Hopfield Network for Pattern Satisfiability Optimization , 2016 .

[7]  Saratha Sathasivam,et al.  Discrete Mutation Hopfield Neural Network in Propositional Satisfiability , 2019, Mathematics.

[8]  Nur Ezlin Zamri,et al.  Modified Imperialistic Competitive Algorithm in Hopfield Neural Network for Boolean Three Satisfiability Logic Mining , 2020 .

[9]  Saratha Sathasivam,et al.  Students’ performance via satisfiability reverse analysis method with Hopfield Neural Network , 2019 .

[10]  Mohd Shareduwan Mohd Kasihmuddin,et al.  Amazon Employees Resources Access Data Extraction via Clonal Selection Algorithm and Logic Mining Approach , 2020, Entropy.

[11]  Barnabás Póczos,et al.  Learning Local Search Heuristics for Boolean Satisfiability , 2019, NeurIPS.

[12]  Alexander K. Hartmann,et al.  Phase transitions of the typical algorithmic complexity of the random satisfiability problem studied with linear programming , 2017, PloS one.

[13]  Saratha Sathasivam,et al.  Accelerating Activation Function for 3- Satisfiability Logic Programming , 2016 .

[14]  Saratha Sathasivam,et al.  Hybrid Genetic Algorithm in the Hopfield Network for Logic Satisfiability Problem , 2017 .

[15]  Saratha Sathasivam,et al.  Robust Artificial Immune System in the Hopfield network for Maximum k-Satisfiability , 2017, Int. J. Interact. Multim. Artif. Intell..

[16]  Saratha Sathasivam,et al.  Upgrading logic programming in hopfield network , 2010 .

[17]  Saratha Sathasivam,et al.  Systematic Satisfiability Programming in Hopfield Neural Network- A Hybrid Expert System for Medical Screening , 2020 .

[18]  Mehmed Kantardzic,et al.  No Free Lunch Theorem for concept drift detection in streaming data classification: A review , 2019, WIREs Data Mining Knowl. Discov..

[19]  Jinwen Ma.  The Stability of the Generalized Hopfield Networks in Randomly Asynchronous Mode , 1997, Neural Networks.

[20]  P. Jaccard.  THE DISTRIBUTION OF THE FLORA IN THE ALPINE ZONE.1 , 1912 .

[21]  Haijun Zhou.  Solution space heterogeneity of the random $K$-satisfiability problem: Theory and simulations , 2010, ArXiv.

[22]  Saratha Sathasivam,et al.  Genetic Algorithm for Restricted Maximum k-Satisfiability in the Hopfield Network , 2016, Int. J. Interact. Multim. Artif. Intell..

[23]  Jianqiang Wang,et al.  A distributed dynamic route guidance approach based on short-term forecasts in cooperative infrastructure-vehicle systems , 2019 .

[24]  Ebrahim Kalani,et al.  Selection of Investment Basis Using Neural Networks in Stock Exchange , 2018 .

[25]  Wan Ahmad Tajuddin Wan Abdullah,et al.  Logic programming on a neural network , 1992, Int. J. Intell. Syst..

[26]  Hossam Faris,et al.  Unsupervised intelligent system based on one class support vector machine and Grey Wolf optimization for IoT botnet detection , 2019, Journal of Ambient Intelligence and Humanized Computing.

[27]  Hamza Abubakar,et al.  Election Algorithm for Random k Satisfiability in the Hopfield Neural Network , 2020, Processes.

[28]  D. Ielmini,et al.  A Spiking Recurrent Neural Network With Phase-Change Memory Neurons and Synapses for the Accelerated Solution of Constraint Satisfaction Problems , 2020, IEEE Journal on Exploratory Solid-State Computational Devices and Circuits.

[29]  Björn Berggren,et al.  Parametric multi-objective energy and cost analysis in the life cycle of nearly zero energy buildings − an exhaustive search approach , 2019, Sustainable Buildings.

[30]  Samy S. Abu-Naser,et al.  Artificial Neural Network for Predicting Animals Category , 2019 .

[31]  Saratha Sathasivam,et al.  Bezier Curves Satisfiability Model in Enhanced Hopfield Network , 2016 .

[32]  Saratha Sathasivam,et al.  Modified Artificial Immune System Algorithm with Elliot Hopfield Neural Network For 3-Satisfiability Programming , 2019 .

[33]  Károly Héberger,et al.  Life beyond the Tanimoto coefficient: similarity measures for interaction fingerprints , 2018, Journal of Cheminformatics.

[34]  P. P. Boriskov,et al.  IoT-Oriented Design of an Associative Memory Based on Impulsive Hopfield Neural Network with Rate Coding of LIF Oscillators , 2020, Electronics.

[35]  E. Aurell,et al.  Behavior of heuristics on large and hard satisfiability problems. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Xuhao Tang,et al.  Discrete Hopfield neural network based indoor Wi-Fi localization using CSI , 2020, EURASIP Journal on Wireless Communications and Networking.

[37]  Yan Wang,et al.  A novel memristive Hopfield neural network with application in associative memory , 2017, Neurocomputing.

[38]  Aneesh Chandran,et al.  Artificial Neural Network for Diagnosing Autism Spectrum Disorder , 2018, 2018 2nd International Conference on Trends in Electronics and Informatics (ICOEI).

[39]  Yongping Wang,et al.  Properties of the satisfiability threshold of the strictly d-regular random (3,2s)-SAT problem , 2020, Frontiers of Computer Science.

[40]  Erik Aurell,et al.  Local search methods based on variable focusing for random K-satisfiability. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  Mohammad Lutfi Othman,et al.  A novel RK4-Hopfield Neural Network for Power Flow Analysis of power system , 2020, Appl. Soft Comput..

[42]  Sun Guang,et al.  Network Traffic Prediction Based on the Wavelet Analysis and Hopfield Neural Network , 2013 .

[43]  Ahmed M. Soliman,et al.  Analyzing patient health information based on IoT sensor with AI for improving patient assistance in the future direction , 2020 .