Dear Fellow Researchers,

Would you kindly pay attention to the article “Non-Orthodox Combinatorial Models Based on Discordant Structures” by the author V. F. Romanov published on arXiv.org: http://arxiv.org/abs/1011.3944 (download: PDF, initial format LaTeX, 12pt).

The article presents a constructive proof of effective resolvability of 3-SAT problem, accompanied by description of a polynomial algorithm created for the named purpose.

The proof uses a unique graph-combinatorial model based on the Boolean formulas representation in the form of structures of compact triplets. The proof procedure required the induction principle applied to special constructive components which are systems of hyperstructures.

This work was developed for a period of 10 years by private initiative independently of my professor duties in Vladimir State University. For this time work has been published in several Russian scientific journals. Also two independent versions of the algorithm in programming languages have been implemented.

The first version was developed in parallel with theoretical positions and had been finished in 2002. On its basis statistical computer-aided experiment which is mentioned in paper was accomplished.

The second version was implemented by my colleagues in the end of 2010. In the course of work they used only ready article, in passing offering remarks to the text for the purpose of improvement of its understanding. Successful realization of the algorithm testified to sufficiency of the material stated in the article. Source code of the program is accessible in Internet under license LGPL version 3: https://github.com/anjlab/sat3, also https://romvf.wordpress.com

The fact of existence of the polynomial algorithm for 3-SAT problem leads to a conclusion that P=NP.

Your opinion and suggestions concerning my work would be of great value for me.

Yours faithfully, the author Vladimir Romanov