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Introducing a Finite State Machine for Processing Collatz Sequences
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Introducing a Finite State Machine for Processing Collatz Sequences

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Abstract:

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 then discuss the possibilities for utilizing this approach for 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.

Info:

Periodical:
International Journal of Pure Mathematical Sciences (Volume 19)
Pages:
10-19
DOI:
https://doi.org/10.18052/www.scipress.com/IJPMS.19.10
Citation:
E. Sultanow et al., "Introducing a Finite State Machine for Processing Collatz Sequences", International Journal of Pure Mathematical Sciences, Vol. 19, pp. 10-19, 2017
Online since:
December 2017
Authors:
Eldar Sultanow, Denis Volkov, Sean Cox
Keywords:
Collatz Conjecture, Double Colored Edges, Graph, State Machine
Export:
RIS, BibTeX, Text
Distribution:
Open Access

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Creative Commons Attribution 4.0 International License

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