Inductively Computable Hierarchies and Inductive Algorithmic Complexity

Inductively Computable Hierarchies and Inductive Algorithmic Complexity

Mark Burgin

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1 University of California

GJCST Volume 16 Issue H1

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Induction is a prevalent cognitive method in science, while inductive computations are popular in many fields of computer and network technology. The most advanced mathematical model of inductive computations and reasoning is an inductive Turing machine, which is natural extension of the most widespread 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. In this paper (Section 3), we study relations between inductively computable sets, inductively recognizable sets, inductively decidable sets and inductively computable functions. In addition (Section 4), we apply the obtained results to algorithmic information theory demonstrating how inductive Turing machines allow obtaining more information for essentially decreasing complexity in comparison with Turing machines.

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References

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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

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No ethics committee approval was required for this article type.

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Mark Burgin. 2016. \u201cInductively Computable Hierarchies and Inductive Algorithmic Complexity\u201d. Global Journal of Computer Science and Technology - H: Information & Technology GJCST-H Volume 16 (GJCST Volume 16 Issue H1): .

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GJCST Volume 16 Issue H1
Pg. 35- 45

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Journal Specifications

Crossref Journal DOI 10.17406/gjcst

Print ISSN 0975-4350

e-ISSN 0975-4172

Keywords

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Classification

F.1.3 F.2.2

Submission ReceivedDecember 14, 2015
RevisedDecember 14, 2015
Peer Review Double Blind
Handling Editor
Accepted January 4, 2016
Published January 15, 2016

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v1.2

Issue date

March 4, 2016

Language

English

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Total Score: 131

Country: United States

Subject: Global Journal of Computer Science and Technology - H: Information & Technology

Authors: Mark Burgin (PhD/Dr. count: 0)

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Publish Date: 2016 03, Fri

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Total Views: 7592

Total Downloads: 2032

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