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 (
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.