Learning the Satisfiability of Ł-clausal Forms

The k-SAT problem for Ł-clausal forms has been found to be NP-complete if \(k\ge 3\). Similar to Boolean formulas in Conjunctive Normal Form (CNF), Ł-clausal forms are important from a theoretical and practical point of views for their expressive power, easy-hard-easy pattern as well as having a phase transition phenomena. In this paper, we investigate predicting the satisfiability of Ł-clausal forms by training different classifiers (Neural Network, Linear SVC, Logistic Regression, Random Forest and Decision Tree) on features extracted from randomly generated formulas. Firstly, a random instance generator is presented and used to generate instances in the phase transition area over 3-valued and 7-valued Lukasiewicz logic. Next, numeric and graph features were extracted from both datasets. Then, different classifiers were trained and the best classifier (Neural Network) was selected for hyper-parameter tuning, after which the mean of the cross-validation scores (CVS) increased from 92.5% to 95.2%.

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