P = NP

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 MExistsAcceptingPath, that determines if there exists an accepting computational path of a polynomial time non-deterministic single-tape Turing machine MNP, is constructed (machine MExistsAcceptingPath is different for each Turing machine MNP). Machine MExistsAcceptingPath 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 MAcceptingPath 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 MExistsAcceptingPath is O(t(n)^{272}) wherein t(n) is an upper bound of the time complexity of machine MNP.