| Autor: |
ГУПАЛ, А. М., ΒΑΓΙC, Ο. Α. |
| Předmět: |
|
| Zdroj: |
Cybernetics & Systems Analysis / Kibernetiki i Sistemnyj Analiz; 2024, Issue 5, p16-19, 4p |
| Abstrakt: |
In the theory of recursive functions, a recursively enumerable (but not recursive) set K{x|xE Wx} is obtained by Cantor’s diagonal method. Based on Diophantine sets, K is expressed by some polynomial that has positive roots. On the contrary, the set K{x|xE Wx} is not recursively enumerable. None of the computable functions can enumerate all the elements of the set K . As a result of the productivity of the set K, a parameter exists for which the polynomial has no positive roots. However, it is impossible to prove their absence since this parameter does not belong to any recursively enumerable set. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
|
