Data Structures and Algorithms

   

On the Equivalence Between P=NP and the Extended Church-Turing Thesis.

Authors: Óscar E. Chamizo Sánchez

Since the mere Church-Turing thesis says that Turing machines can simulate any computational device, but perhaps at the cost of an exponential blowup in time and/or space, the Extended Church-Turing Thesis (ECT for short) states that every physically realizable computational device can be efficiently simulated by Turing machines. Unlike the Church-Turing Thesis, which computer science conventional wisdom appears to think is true, the Extended Church-Turing Thesis is widely believed to be false just as it happens with the P=NP conjecture. In this paper we present an interesting extension from our seminal papers A new approach: A hardware device model solving TSP in O(n2) time and Efficiently solving Traveling Salesman Problem in a computer network. (Internet), proving the equivalence between ECT and P=NP. In section 1 we go directly to a physically feasible model and prove mathematically its validity. In section 2 we explain the basic ideas behind the physical model. In section 3 we prove the equivalence between the conjecture P=NP and the ECT thesis.

Comments: 3 Pages.

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[v1] 2018-05-04 09:41:30

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