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Topic: Matiyasevich's theorem

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In the News (Thu 23 May 13)

 Matiyasevich's theorem: Definition and links. Matiyasevich's theorem has since been used to prove that many problems from calculus and differential equations are unsolvable. Matiyasevich's theorem, proven in 1970 by Yuri Matiyasevich[?], implies that Hilbert's tenth problem is unsolvable. Matiyasevich's theorem itself is somewhat more general than the unsolvability of the Tenth Problem; it can be stated as "Every recursively enumerable set is Diophantine ". www.encyclopedian.com /ma/Matiyasevichs-theorem.html

 AMCA: Diophantine flavour of Kolmogorov complexity by Yuri Matiyasevich AMCA: Diophantine flavour of Kolmogorov complexity by Yuri Matiyasevich Patrick Cegielski (France), Hrant Marandjian (Armenia), Yuri Matiyasevich (Russia), Jean-Pierre Ressayre (France), Denis Richard (France), Yuri Shoukourian (Armenia), Igor Zaslavsky (Armenia) The DPRM-theorem can serve as a bridge between Theoretical Computer Science and Number Theory. at.yorku.ca /c/a/n/i/11.htm

 Rewriting383---rigid_E_unification ----------------------------------------------- Simultaneous Rigid \$E\$-Unification is not so Simple Anatoli Degtyarev Yuri Matiyasevich Andrei Voronkov Simultaneous rigid \$E\$-unification has been introduced in the area of theorem proving with equality. www.dcs.st-and.ac.uk /~sal/Rewriting/383.html

 Diophantus of Alexandria and the 10-th Problem of Hilbert – Dy The Importance was that its solution is the main step in solution of general quadratic Diophantine equations in two variables and useful for Matiyasevich theorem on non-existence of the general algorithm for solving Diophantine equations. Yuri Matiyasevich and the 10-th Problem of Hilbert Then in 1970 Yuri Matiyasevich solved the 10-th Problem of Hilbert showing that such an algorithm that can solve any Diophantine equation does not exist ! www.mlahanas.de /Greeks/Diophantus.htm

 The Third Culture - Chapter 14 There's a famous theorem, due to Yuri Matiyasevich, which proves that there's no computational way of answering this question in general. That is, do the equations have integer solutions?" That question — yes or no, for any particular example — is not one a computer could answer in any finite amount of time. In particular cases, you might be able to give an answer by means of some algorithmic procedure. www.edge.org /documents/ThirdCulture/v-Ch.14.html

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