Decidability of NP-Complete Problems - Vagis, A. A.; Gupal, A. M. (Cybernetics and systems analysis, 2022)
An analysis of the undecidability of Diophantine equations showed that problems of recognition of the properties of the NP class are decidable, i.e., a non-deterministic algorithm or exhaustive search at the problem input gives a positive or negative answer. For polynomial Diophantine equations, such a non-deterministic algorithm does not exist. A simple version of Gödel’s theorem on the incompleteness of arithmetic follows from the undecidability of Diophantine equations.