التفاصيل البيبلوغرافية
| العنوان: |
Polynomial Analogue of Gandy’s Fixed Point Theorem |
| المؤلفون: |
Sergey Goncharov, Andrey Nechesov |
| المصدر: |
Mathematics; Volume 9; Issue 17; Pages: 2102 |
| بيانات النشر: |
Multidisciplinary Digital Publishing Institute |
| سنة النشر: |
2021 |
| المجموعة: |
MDPI Open Access Publishing |
| مصطلحات موضوعية: |
polynomial computability, p-computability, Gandy’s fixed point theorem, semantic programming, polynomial operators, Δ 0 p , computer science |
| الوصف: |
The paper suggests a general method for proving the fact whether a certain set is p-computable or not. The method is based on a polynomial analogue of the classical Gandy’s fixed point theorem. Classical Gandy’s theorem deals with the extension of a predicate through a special operator ΓΦ(x)Ω∗ and states that the smallest fixed point of this operator is a Σ-set. Our work uses a new type of operator which extends predicates so that the smallest fixed point remains a p-computable set. Moreover, if in the classical Gandy’s fixed point theorem, the special Σ-formula Φ(x¯) is used in the construction of the operator, then a new operator uses special generating families of formulas instead of a single formula. This work opens up broad prospects for the application of the polynomial analogue of Gandy’s theorem in the construction of new types of terms and formulas, in the construction of new data types and programs of polynomial computational complexity in Turing complete languages. |
| نوع الوثيقة: |
text |
| وصف الملف: |
application/pdf |
| اللغة: |
English |
| Relation: |
Computational and Applied Mathematics; https://dx.doi.org/10.3390/math9172102 |
| DOI: |
10.3390/math9172102 |
| الاتاحة: |
https://doi.org/10.3390/math9172102 |
| Rights: |
https://creativecommons.org/licenses/by/4.0/ |
| رقم الانضمام: |
edsbas.51B09E53 |
| قاعدة البيانات: |
BASE |