Inductively Computable Sets and Functions

Authors

  • Mark Burgin Department of Mathematics, University of California, Los Angeles, 405 Hilgard Ave, Los Angeles, CA 90095

Keywords:

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

Abstract

Inductive computations are used in many areas of computer and network technology. Inductive reasoning form the base for scientific exploration. A mathematical model of inductive computations and reasoning is called an inductive Turing machine, which is 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. In this paper, we study properties of these sets and functions.Cite this ArticleMark Burgin. Inductively Computable Sets and Functions. Journal of Computer Technology & Applications. 2016; 7(1): 12–21p.  

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Published

2016-02-12

Issue

Vol. 7 No. 1 (2016)

Section

Research Articles

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