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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 26 / No. 1: Twenty-Sixth AAAI Conference on Artificial Intelligence

Predicting Satisfiability at the Phase Transition

March 8, 2023

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Authors

Lin Xu

University of British Columbia


Holger Hoos

University of British Columbia


Kevin Leyton-Brown

University of British Columbia


DOI:

10.1609/aaai.v26i1.8142


Abstract:

Uniform random 3-SAT at the solubility phase transition is one of the most widely studied and empirically hardest distributions of SAT instances. For 20 years, this distribution has been used extensively for evaluating and comparing algorithms. In this work, we demonstrate that simple rules can predict the solubility of these instances with surprisingly high accuracy. Specifically, we show how classification accuracies of about 70% can be obtained based on cheaply (polynomial-time) computable features on a wide range of instance sizes. We argue in two ways that classification accuracy does not decrease with instance size: first, we show that our models' predictive accuracy remains roughly constant across a wide range of problem sizes; second, we show that a classifier trained on small instances is sufficient to achieve very accurate predictions across the entire range of instance sizes currently solvable by complete methods. Finally, we demonstrate that a simple decision tree based on only two features, and again trained only on the smallest instances, achieves predictive accuracies close to those of our most complex model. We conjecture that this two-feature model outperforms random guessing asymptotically; due to the model's extreme simplicity, we believe that this conjecture is a worthwhile direction for future theoretical work.

Topics: AAAI

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HOW TO CITE:

Lin Xu|| Holger Hoos|| Kevin Leyton-Brown Predicting Satisfiability at the Phase Transition Proceedings of the AAAI Conference on Artificial Intelligence, 26 (2012) 584.

Lin Xu|| Holger Hoos|| Kevin Leyton-Brown Predicting Satisfiability at the Phase Transition AAAI 2012, 584.

Lin Xu|| Holger Hoos|| Kevin Leyton-Brown (2012). Predicting Satisfiability at the Phase Transition. Proceedings of the AAAI Conference on Artificial Intelligence, 26, 584.

Lin Xu|| Holger Hoos|| Kevin Leyton-Brown. Predicting Satisfiability at the Phase Transition. Proceedings of the AAAI Conference on Artificial Intelligence, 26 2012 p.584.

Lin Xu|| Holger Hoos|| Kevin Leyton-Brown. 2012. Predicting Satisfiability at the Phase Transition. "Proceedings of the AAAI Conference on Artificial Intelligence, 26". 584.

Lin Xu|| Holger Hoos|| Kevin Leyton-Brown. (2012) "Predicting Satisfiability at the Phase Transition", Proceedings of the AAAI Conference on Artificial Intelligence, 26, p.584

Lin Xu|| Holger Hoos|| Kevin Leyton-Brown, "Predicting Satisfiability at the Phase Transition", AAAI, p.584, 2012.

Lin Xu|| Holger Hoos|| Kevin Leyton-Brown. "Predicting Satisfiability at the Phase Transition". Proceedings of the AAAI Conference on Artificial Intelligence, 26, 2012, p.584.

Lin Xu|| Holger Hoos|| Kevin Leyton-Brown. "Predicting Satisfiability at the Phase Transition". Proceedings of the AAAI Conference on Artificial Intelligence, 26, (2012): 584.

Lin Xu|| Holger Hoos|| Kevin Leyton-Brown. Predicting Satisfiability at the Phase Transition. AAAI[Internet]. 2012[cited 2023]; 584.


ISSN: 2374-3468


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