Diagonalization of Polynomial-Time Turing Machines Via Nondeterministic Turing Machine

10/12/2021

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by   Tianrong Lin, et al.

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The diagonalization technique was invented by Georg Cantor to show that there are more real numbers than algebraic numbers, and is very important in computer science. In this work, we enumerate all polynomial-time deterministic Turing machines and diagonalize over all of them by an universal nondeterministic Turing machine. As a result, we obtain that there is a language L_d not accepted by any polynomial-time deterministic Turing machines but accepted by a nondeterministic Turing machine working within O(n^k) for any k∈ℕ_1. By this, we further show that L_d∈𝒩𝒫 . That is, we present a proof that 𝒫 and 𝒩𝒫 differ.