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Introducing a Finite State Machine for processing Collatz Sequences

  • The present work will introduce a Finite State Machine (FSM) that processes any Collatz Sequence; further, we will endeavor to investigate its behavior in relationship to transformations of a special infinite input. Moreover, we will prove that the machine’s word transformation is equivalent to the standard Collatz number transformation and subsequently discuss the possibilities for use of this approach at solving similar problems. The benefit of this approach is that the investigation of the word transformation performed by the Finite State Machine is less complicated than the traditional number-theoretical transformation.

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Author:Eldar SultanowORCiDGND, Denis Volkov, Sean Cox
Document Type:Report
Date of first Publication:2017/09/06
Year of Completion:2017
Publishing Institution:Universität Potsdam
Release Date:2017/09/06
Tag:Collatz Conjecture; Double Colored Edges; Graph; State Machine
Edition:1st version
Organizational units:Wirtschafts- und Sozialwissenschaftliche Fakultät / Wirtschaftswissenschaften
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC Classification:11-XX NUMBER THEORY
Collections:Universität Potsdam / Sondersammlungen / Introducing a Finite State Machine for processing Collatz Sequences / First version
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht
Notes extern:Subsequent version of the paper