Data Structures and Algorithms


Polynomial 3-SAT-Solver

Authors: Matthias Mueller

Four different polynomial 3-SAT algorithms named "Algorithm A/B/C/D[M]" are provided:

v1: "Algorithm A":  Obsolete, please ignore.
v2: "Algorithm B":  Obsolete. Published in December 2013. Never failed for millions of test runs. Proof of correctness needs to be improved. Mr. M. Prunescu's paper 'About a surprizing computer program of Matthias Mueller' is about this Algorithm B.
v3: "Algorithm C":  Obsolete, please ignore.
v4: "Algorithm D‑1.0":  Newest and best algorithm. Never failed in tests. Related paper v4 contains a detailed description of this polynomial 3-SAT solving algorithm, an extensive proof of correctness and a link where you can download my compiled demo C++ implementation (with source code) for Windows and Linux, an alternative polynomial solver version, and an additional tool program.
v5: "Algorithm D‑1.1":  Very same algorithm as v4, but better explained and with a re-written, completely new part of the proof of correctness.
v6: "Algorithm D‑1.1":  Some helpful improvements (compared to v5).
v7: "Algorithm D‑1.2":  Paper from May 22nd, 2016.
v8: "Algorithm D‑1.3":  Parts of the proof of correctness have been replaced by a completely re-written, more detailed variant.
v9: "Algorithm D‑1.3":  Please read this version for a figurative, linguistic description of the algorithm. Another part of the proof of correctness has been made more detailed.
vA: "Algorithm DM‑1.0":  Completely re-written document. Still describes algorithm D, but as short as possible and in mathematical notation.
vB: "Algorithm DM‑2.0":  Heavily revised and extended vA document. A much more precise notation is used (compared to vA) and most formulas are now comprehensively commented and explained. Might be easier to understand for learned readers, while others prefer v9 (D-1.3).
vC: "Algorithm DM‑2.1":  Please read this version for a precise, mathematical description of the algorithm. Best paper of all. Compared to DM-2.0, three substantial extensions have been added: Why the algorithm does NOT have the restrictions of a logical resolution, that the polynomial solver correctly solved the pigeon hole problem for n=6 ("PH6"), and what the ideas behind the three rules of the polynomial algorithm are.
You can also visit for latest updates and news, and the zip file containing the Windows/Linux demo implementation.

Comments: 45 Pages.

Download: PDF

Submission history

[v1] 2012-12-17 07:58:51
[v2] 2013-12-13 07:21:02
[v3] 2015-05-10 11:38:40
[v4] 2015-11-11 11:19:40
[v5] 2016-02-24 18:28:19
[v6] 2016-05-10 11:37:43
[v7] 2016-06-15 08:46:27
[v8] 2017-01-22 18:01:27
[v9] 2017-01-23 12:05:27
[vA] 2017-11-05 11:10:50
[vB] 2018-04-14 16:53:02
[vC] 2018-11-17 14:19:06

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