My Math Forum P equals NP because 3SAT reduces to solving linear equations

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 May 4th, 2013, 12:55 AM #2 Senior Member   Joined: Jan 2013 Posts: 209 Thanks: 3 Re: P equals NP because 3SAT reduces to solving linear equat EDIT: n*(n-1)*(n-2)/6 scalar vars should be 8*n*(n-1)*(n-2)/6 scalar vars, same as number of nodes.
 May 4th, 2013, 02:51 AM #3 Senior Member   Joined: Jan 2013 Posts: 209 Thanks: 3 Re: P equals NP because 3SAT reduces to solving linear equat Or to say it a simpler way, sumsToOne(set of probability vars) constraint is in NP because it can represent bayesian nodes, NAND, Rule 110, and 3SAT as sumsToOne constraints on combinations of their 3-way conditional vars, in some cases the opposite set of conditionals with the same set on another side. sumsToOne is in NP, and sumsToOne is a linear equation.... x + y + z ... = 1. Since bayesian weights translate to squared vars in quantum math which also sums to 1, sumsToOne in that context is the equation of a unit hypersphere. Can you make all the hyperspheres have radius 1 simultaneously, even though they share some perpendicular dimensions but not others? Or lets keep it simple... All of computing theory reduces to the sumsToOne constraint. Rule 110 moves down to second place as simplest universal math operator for containing at least the 8 bits of data in its name. sumsToOne is in the laws of physics. All probability amplitudes must sum to 1.
 May 4th, 2013, 11:51 AM #4 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: P equals NP because 3SAT reduces to solving linear equat Solving systems of integer equations is not known or believed to be in P.
 May 22nd, 2013, 05:54 PM #5 Senior Member   Joined: Jan 2013 Posts: 209 Thanks: 3 Re: P equals NP because 3SAT reduces to solving linear equat I was afraid of that, but it looked so simple at the time. I guess we just have one more translation, which at least looks easier to solve.

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