P = NP
release_7np6wo6m35gsfm6jsnbbx46mtq
by
Sergey V. Yakhontov
2012
Abstract
The present work proves that P=NP. The proof, presented in this work, is a
constructive one: the program of a polynomial time deterministic multi-tape
Turing machine M_ExistsAcceptingPath, that determines if there exists an
accepting computational path of a polynomial time non-deterministic single-tape
Turing machine M_NP, is constructed (machine M_ExistsAcceptingPath is different
for each Turing machine M_NP). Machine M_ExistsAcceptingPath is based on
reduction to problem LP (linear programming) instead of reduction to problem
3-CNF-SAT which is commonly used. In more detail, machine M_AcceptingPath uses
a reduction of the initial string problem to another string problem TCPE
(defined in the paper) that is NP-complete and decidable in polynomial time.
The time complexity of machine M_ExistsAcceptingPath is O(t(n)^272) wherein
t(n) is an upper bound of the time complexity of machine M_NP.
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