Abstract
We present an improved algorithm for the general satisfiability problem. We introduce a new measure, the l-value, for a Boolean formula \(\cal F\), which is defined based on weighted variable frequencies in the formula \(\cal F\). We then develop a branch-and-search algorithm for the satisfiability problem that tries to maximize the decreasing rates in terms of the l-value during the branch-and-search process. The complexity of the algorithm in terms of the l-value is finally converted into the complexity in terms of the total length L of the input formula, resulting in an algorithm of running time O(20.0911L) = O(1.0652L) for the satisfiability problem, improving the previous best upper bound O(20.0926L) = O(1.0663L) for the problem.
This work was supported in part by the National Science Foundation under the Grant CCF-0830455.
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Chen, J., Liu, Y. (2009). An Improved SAT Algorithm in Terms of Formula Length. In: Dehne, F., Gavrilova, M., Sack, JR., Tóth , C.D. (eds) Algorithms and Data Structures. WADS 2009. Lecture Notes in Computer Science, vol 5664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03367-4_13
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