Abstract
Matthias Müller published on the net a C++ code and a text describing the implemented algorithm. He claimed that the algorithm “maybe” solves the NP-complete problem 3-SAT in polynomial time. The program decided correctly so far the solvability for all instances that have been checked. This intriguing fact must be understood. In order to achieve this goal, we introduce the graph of all possible k-SAT clauses with edges connecting every two non-conflicting clauses. We prove that a k-SAT instance I is satisfiable if and only if there is a maximal clique of the clause graph that does not intersect I.
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References
M. Müller, Polynomial SAT-solver. http://vixra.org/author/matthias_mueller
M.R. Garey, D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, (W.H. Freeman & Co., 1979)
B. Aspvall, M.F. Plass, R.E. Tarjan, A linear-time algorithm for testing the truth of certain quantified boolean formulas. Inf. Process. Lett. 8(3), 121–123 (1979)
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© 2016 Springer International Publishing Switzerland
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Prunescu, M. (2016). About a Surprising Computer Program of Matthias Müller. In: Adiprasito, K., Bárány, I., Vilcu, C. (eds) Convexity and Discrete Geometry Including Graph Theory. Springer Proceedings in Mathematics & Statistics, vol 148. Springer, Cham. https://doi.org/10.1007/978-3-319-28186-5_9
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DOI: https://doi.org/10.1007/978-3-319-28186-5_9
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