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JOURNALS // Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia // Archive

Dokl. RAN. Math. Inf. Proc. Upr., 2024 Volume 518, Pages 35–39 (Mi danma548)

MATHEMATICS

Sufficient condition for polynomial solvability of random 3-CNF formulas

S. I. Uvarov

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia

Abstract: This paper is devoted to the localisation of random 3-CNF formulas that are polynomially solvable by the resolution algorithm. It is shown that random formulas with the number of clauses proportional to the square of the number of variables, are polynomially solvable with probability close to unity when the proportionality coefficient exceeds the found threshold.

Keywords: 3-CNF, clause, resolution, complexity, satisfiability problem.

UDC: 510

Presented: S. N. Vassilyev
Received: 22.04.2024
Revised: 11.06.2024
Accepted: 16.07.2024

DOI: 10.31857/S2686954324040067


 English version:
Doklady Mathematics, 2024, 110:1, 323–327

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© Steklov Math. Inst. of RAS, 2025