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

• Published in: IEEE access Vol. 9; pp. 50831 - 50845
• Main Authors: Karim, Syed Anayet, Zamri, Nur Ezlin, Alway, Alyaa, Mohd Kasihmuddin, Mohd Shareduwan, Md Ismail, Ahmad Izani, Mansor, Mohd. Asyraf, Abu Hassan, Nik Fathihah
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Artificial neural networks; Biological neural networks; Discrete hopfield neural network; Hopfield neural networks; Indexes; Logic; Neural networks; Neurons; Performance evaluation; random 3 satisfiability; random <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">k satisfiability; Search algorithms; Solution space; Systematics
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2021.3068998

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 ( RAN3SAT ) 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 RAN3SAT 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 RAN3SAT was able to be implemented in DHNN, and each logical combination has its characteristics. Nonetheless, RAN3SAT 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 RAN3SAT consists of various logic combinations that behave as input language to transform raw data into informative output.