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.

Novel Hopfield Neural Network Model with Election Algorithm for Random 3 Satisfiability

“…In this case, EA provides solution partitioning mechanism to reduce the impact of high-density capacity due to third order logic by increasing the probability of the network to obtain the correct assignment for first order logic. This view has been supported by the recent simulation work by [28]. This work showed the learning capacity of RAN3SAT in HNN reduced dramatically when the number of first order logic increases.…”

“…The final state of Equation ( 4) can be analyzed by computing the final energy and comparing it with the absolute minimum energy. As pointed out in [28,33], the main weakness of HNN is the lack of symbolic rule that governs the network. According to [28], the selection of ψ = 0 will ensure the network dynamic reach the nearest optimal solution.…”

“…As pointed out in [28,33], the main weakness of HNN is the lack of symbolic rule that governs the network. According to [28], the selection of ψ = 0 will ensure the network dynamic reach the nearest optimal solution. Lack of effective symbolic rule makes HNN, numerically difficult to obtain the absolute minimum energy.…”

Modified 2 Satisfiability Reverse Analysis Method via Logical Permutation燨perator

“…By adapting various forms of 2SAT logical structure during the learning phase of HNN, P2SATRA outperfomed the 2SATRA, E2SATRA and RA approaches when being measured with the performance metrics such as the accuracy, precision, sensitivity, F-Score and MCC after the logic mining analysis with 11 different real datasets. For instance, it will be interesting to infuse different logical rule such as Maximum Satisfiability [20], Y-Type Random Satisfiability [8], G-Type Random Satisfiability [9] and Random k Satisfiability [5]. In terms of network architecture, it will be interesting if other learning mechanism such as in [21,22] were embeded into logic mining.…”

“…This shows that the interpretation of the 2SAT logical rule in DHNN can be further optimized using optimization algorithm. The implementation of 2SAT in various network inspires the emergence of other useful logic such as [5][6][7][8][9] in doing DHNN. Various type of logical rule creates optimal modelling of DHNN that has wide range of behavior.…”