Inductively Computable Sets and Functions

Abstract

Abstract
Inductive computations are used in many areas of computer and network technology. Inductive reasoning forms the base for scientific exploration. A mathematical model of inductive computations and reasoning is called an inductive Turing machine, which is a natural extension of the most popular model of computing devices and computations - Turing machine. In comparison with Turing machines, inductive Turing machines represent the next step in the development of computer science providing better models for contemporary computers and computer networks. Inductive Turing machines generate inductively computable sets, separate inductively recognizable sets, discern inductively decidable sets and compute inductively computable functions. In this paper, we study properties of these sets and functions.

Keywords: Inductive computation, Turing machine, Inductive Turing machine, Inductive computability, Inductive recognizability, Inductive decidability

Cite this Article
Mark Burgin. Inductively Computable Sets and Functions. Journal of Computer Technology & Applications. 2016; 7(1): 12–21p.