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I have an interesting algorithm for 3SAT in mind that I wanted to implement but was not able to code for the same so unable to see if it really works. The algorithm is defined in a Microsoft Word file here: DropBox Link for 3SAT algorithm I do not know if this algorithm really works and if it does what is its complexity. I would really like to know about its complexity though. Please help me regarding this as if it is in polynomial time then I would have proved P=NP!

vinaych
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    I think you should describe your algorithm here, not just point to external site. – piotrekg2 Sep 03 '15 at 12:40
  • No offense, but you should probably learn more CS if you're trying to take on P vs NP. Whatever the answer is, it's not going to be this easy. – harold Sep 03 '15 at 13:18

2 Answers2

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As the description of your algorithm states,

this method may take considerable amount of time as every time the number of rows might get multiplied by 2 (This comes out to be 2m where m is number of clauses)

Hence the worst-case running time of the algorithm is exponential, not polynomial. You are hoping that in many cases the running time will be shorter due to happy coincidences in the input, but worst-case running time is how the P vs NP question is assessed.

David K
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May I suggest you read my paper http://arxiv.org/ftp/arxiv/papers/1411/1411.2901.pdf There you will find a common splitting mechanism to determine satisfiability which apparently is similar to your procedure. The procedure is polynomial (actually linear) in each step but the problem is that the formula length blows up in each step. (As pointed out in one of the answers to your question). In the paper I have addressed the question whether and under which circumstances this blow up is prevented systematically.

bernd s.
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