کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4661938 1633475 2013 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Conditional computability of real functions with respect to a class of operators
ترجمه فارسی عنوان
محاسبه پذیری شرطی توابع حقیقی با توجه به یک کلاس از اپراتورها
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
چکیده انگلیسی

For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect to this class. These two computability notions are natural generalizations of certain notions introduced in a previous paper co-authored by Andreas Weiermann and in another previous paper by the same authors, respectively. Under certain weak assumptions about the class in question, we show that conditional computability is preserved by substitution, that all conditionally computable real functions are locally uniformly computable, and that the ones with compact domains are uniformly computable. The introduced notions have some similarity with the uniform computability and its non-uniform extension considered by Katrin Tent and Martin Ziegler, however, there are also essential differences between the conditional computability and the non-uniform computability in question.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 164, Issue 5, May 2013, Pages 550-565