@MISC{Gubin09apolynomial, author = {Sergey Gubin}, title = {A Polynomial Time Algorithm for SAT}, year = {2009} }

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Abstract

We define a relation of compatibility on partial true assignments using the system’s equations. The relation is a Boolean matrix- the compatibility matrix. We deplete the matrix eliminating relations between those partial true assignments which are not parts of a solution of the whole system. The depletion transforms the relation of compatibility on the set of partial true assignments into the relation of “they are parts of one solution of the system” on the set. The relation is a Boolean matrix- the general solution of a Boolean system. Values “true ” in the general solution indicate which partial true assignments can be extrapolated to a full solution and in which “directions” the extrapolation has to be done. We use the method and solve SAT.