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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| Vydáno v: | Cybernetics and systems analysis Ročník 58; číslo 6; s. 914 - 916 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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New York
Springer US
01.11.2022
Springer Springer Nature B.V |
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| ISSN: | 1060-0396, 1573-8337 |
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| Abstract | 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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| AbstractList | 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. 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 Godel's theorem on the incompleteness of arithmetic follows from the undecidability of Diophantine equations. 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 Godel's theorem on the incompleteness of arithmetic follows from the undecidability of Diophantine equations. Keywords: NP-complete problems, Diophantine equations, non-deterministic algorithm. |
| Audience | Academic |
| Author | Gupal, A. M. Vagis, A. A. |
| Author_xml | – sequence: 1 givenname: A. A. surname: Vagis fullname: Vagis, A. A. email: valexdep135@gmail.com organization: V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine – sequence: 2 givenname: A. M. surname: Gupal fullname: Gupal, A. M. organization: V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine |
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| Cites_doi | 10.1145/800157.805047 10.1017/CBO9781139171496 |
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| Keywords | Diophantine equations NP-complete problems non-deterministic algorithm |
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| References | MatiyasevichYVDiophantine setsUspekhi Mat. Nauk1971225185222441711 M. Gary and L. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, A Series of Books in the Mathematical Sciences, W. H. Freeman and Co., San Francisco (1979). N. Cutland, Computability: An Introduction to Recursive Function Theory, Cambridge Univ. Press (1980). S. A. Cook, “The complexity of theorem-proving procedures,” in: Proc. 3rd Ann. ACM Symp. on Theory of Computing Association for Computing Machinery, New York (1971), pp. 151–158. 524_CR4 YV Matiyasevich (524_CR3) 1971; 22 524_CR2 524_CR1 |
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| SubjectTerms | Algorithms Analysis Artificial Intelligence Control Diophantine equation Mathematical analysis Mathematics Mathematics and Statistics Polynomials Processor Architectures Software Engineering/Programming and Operating Systems Systems Theory |
| Title | Decidability of NP-Complete Problems |
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