Decidability of NP-Complete Problems

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, suc...

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Bibliographic Details
Published in:Cybernetics and systems analysis Vol. 58; no. 6; pp. 914 - 916
Main Authors: Vagis, A. A., Gupal, A. M.
Format: Journal Article
Language:English
Published: New York Springer US 01.11.2022
Springer
Springer Nature B.V
Subjects:
Algorithms
Analysis
Artificial Intelligence
Control
Diophantine equation
Mathematical analysis
Mathematics
Mathematics and Statistics
Polynomials
Processor Architectures
Software Engineering/Programming and Operating Systems
Systems Theory
Diophantine equations
NP-complete problems
non-deterministic algorithm
ISSN:1060-0396, 1573-8337
Online Access:Get full text
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Summary: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.
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ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-023-00524-y