Random K Satisfiability has overcome a lack of interpretation by introducing a flexible structure and generating various solutions which eventually reach global minimum solutions. It is one of the most essential non-systematic logics in the field of artificial neural network research, which discusses the problem of knowledge in logical rules. S-type Random k satisfiability introduces a new non-systematic instruction logic integrated into the Hopfield neural network. Applying the probability distribution of data to introduce the suitable logic structure of data that addresses the prevailing attribute, by using a different range of logic probability with a fixed proportion. This article discusses the flexibility of S-type Random k satisfiability to respond to the data distribution by introducing a variety of systematic and non-systematic models that can be created by applying a different range of probability distributions of data in logic. The performance of the different models in order to reduce the cost function in the Hopfield neural network was investigated by the famous performance matrices in learn and test phase. The overall analysis showed the impact of various values of the probability distribution of data to ship the logic in S-type Random k satisfiability in the Hopfield neural network.

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