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Fri, 06 Dec 2019 18:57:12 +0200Fri, 06 Dec 2019 18:57:12 +0200Collatz Sequences in the Light of Graph Theory
https://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/43008
The Collatz conjecture is a number theoretical problem, which has puzzled countless researchers using myriad approaches. Presently, there are scarcely any methodologies to describe and treat the problem from the perspective of the Algebraic Theory of Automata. Such an approach is promising with respect to facilitating the comprehension of the Collatz sequences "mechanics". The systematic technique of a state machine is both simpler and can fully be described by the use of algebraic means.
The current gap in research forms the motivation behind the present contribution. The present authors are convinced that exploring the Collatz conjecture in an algebraic manner, relying on findings and fundamentals of Graph Theory and Automata Theory, will simplify the problem as a whole.Eldar Sultanow; Christian Koch; Sean Coxpreprinthttps://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/43008Wed, 12 Jun 2019 18:57:12 +0200Introducing a Finite State Machine for processing Collatz Sequences
https://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/40473
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.Eldar Sultanow; Denis Volkov; Sean Coxpreprinthttps://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/40473Fri, 08 Dec 2017 12:11:21 +0100Introducing a Finite State Machine for processing Collatz Sequences
https://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/39922
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.Eldar Sultanow; Denis Volkov; Sean Coxpreprinthttps://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/39922Wed, 06 Sep 2017 16:13:55 +0200