A real function is a prescription which assignes values to arguments. The notation y = f (x) means that to the value x of the argument, the function f assigns the value y. Sometimes we also use the notation f : x ↦ y, in words, the function f sends x to y..
Complexity theory is basically the study of what's hard or easy to solve with a computer. In it, the key thing is how the number of steps it takes to solve a problem grows with the size of the input.
$74.99In stockAbout this book. Starting with Cook's pioneering work on NP-completeness in 1970, polynomial complexity theory, the study of polynomial-time com putability, has Table of contentsAbout this book
$74.99In stockOn the one hand, it bridges the gap between the abstract approach of recursive function theory and the concrete approach of analysis of algorithms. It extends Table of contentsAbout this book
Starting with Cook's pioneering work on NP-completeness in 1970, polynomial complexity theory, the study of polynomial-time com putability, has quickly emerged as the new foundation of algorithms. Google BooksOriginally published: 1991Author: Ker-I Ko
Mathematical function that can be computed by a program
Computable functions are the basic objects of study in computability theory. Computable functions are the formalized analogue of the intuitive notion of algorithms, in the sense that a function is computable if there exists an algorithm that can do the job of the function, i.e. given an input of the function domain it can return the corresponding output. Computable functions are used to discuss computability without referring to any concrete model of computation such as Turing machines or register machines. Any definition, however, must make reference to some specific model of computation but all valid definitions yield the same class of functions. Particular models of computability that give rise to the set of computable functions are the Turing-computable functions and the general recursive functions.
Function computable with bounded loops
In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all for loops. Primitive recursive functions form a strict subset of those general recursive functions that are also total functions.
Non algebraically closed field whose extension by sqrt(–1) is algebraically closed
In mathematics, a real closed field is a field F that has the same first-order properties as the field of real numbers. Some examples are the field of real numbers, the field of real algebraic numbers, and the field of hyperreal numbers.
Complexity theory of real functions
Concept in computability theory
In computability theory, the theory of real computation deals with hypothetical computing machines using infinite-precision real numbers. They are given this name because they operate on the set of real numbers. Within this theory, it is possible to prove interesting statements such as The complement of the Mandelbrot set is only partially decidable.
