Real recursive functions and their hierarchy
نویسندگان
چکیده
منابع مشابه
Real recursive functions and their hierarchy
In the last years, recursive functions over the reals (Theoret. Comput. Sci. 162 (1996) 23) have been 9 considered, first as a model of analog computation, and second to obtain analog characterizations of classical computational complexity classes (Unconventional Models of Computation, UMC 2002, 11 Lecture Notes in Computer Science, Vol. 2509, Springer, Berlin, pp. 1–14). However, one of the op...
متن کاملReal Recursive Functions and Real Extensions of Recursive Functions
Recently, functions over the reals that extend elementarily computable functions over the integers have been proved to correspond to the smallest class of real functions containing some basic functions and closed by composition and linear integration. We extend this result to all computable functions: functions over the reals that extend total recursive functions over the integers are proved to...
متن کاملBeyond Recursive Real Functions
All the recursive real functions are continuous; in fact all the B-recursive real functions are continuous for any oracle B, simply because Turing Machines computing them are nite objects. But simple functions like step functions have to be in some sense be \easy" if they have recursive values and break points, although by our usual deeni-tion, they are not computable at all. So it seems unfair...
متن کاملA Hierarchy of primitive recursive sequence functions
— In this paper we give a characterization of primitive recursive functions ƒ : N~* N{r^0, s>0) and define a Hierarchy of classes b^O) of these functions by a syntactic measure ofeomplexity. The behavior ofthe classes J^a+b^ respect to different operators is also analyzed. The classes J^ + b coincide with the ones ofCleavé's hierarchy for a^2,b^0 and give a refinement of the Meyer-Ri...
متن کاملReal Recursive Functions and Baire Classes
Recursive functions over the reals [6] have been considered, first as a model of analog computation, and second to obtain analog characterizations of classical computational complexity classes [2]. However, one of the operators introduced in the seminal paper by Cris Moore (in 1996), the minimalization operator, creates some difficulties: (a) although differential recursion (the analog counterp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Complexity
سال: 2004
ISSN: 0885-064X
DOI: 10.1016/j.jco.2004.06.001