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

Abstract

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 ( $k = 1, 3, k =2, 3$ , and $k =1$ , 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.

Keywords

• Discrete hopfield neural network
• k satisfiability%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> 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</italic> satisfiability
• random 3 satisfiability