# The Collatz process embeds a base conversion algorithm

@inproceedings{Sterin2020TheCP,
title={The Collatz process embeds a base conversion algorithm},
author={Tristan St'erin and Damien Woods},
booktitle={RP},
year={2020}
}
• Published in RP 14 July 2020
• Mathematics, Computer Science

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## References

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This paper implements the algorithm which generates the regular expression, $\texttt{reg}_k(x)$ for any $x$ and \$k, and gives a new exploratory tool for further study of the Collatz graph in binary.

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• Mathematics, Computer Science
Developments in Language Theory
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It is remarked that the automaton F×3 that multiplies by 3 can be slightly modified to simulate the Collatz function and several open problems concerning pattern generation by cellular automata are state.

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• Mathematics, Computer Science
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This work investigates the odd Collatz sequences and uses binary arithmetic to provide proof of some results in the 3n + 1 problem and presents a sequence of sets whose set-theoretic limit approaches the set containing only 1.

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This is the second part of a work devoted to the study of linear Mahler systems in several variables from the perspective of transcendence and algebraic independence. From the lifting theorem

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The class of freezing cellular automata, those where the state of a cell can only increase according to some order on states, is introduced and it is shown that, if their definition imposes strong constraints on their possible dynamics, they still can produce complex computational behaviors, even in dimension 1.

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• Mathematics
CiE
• 2020
It is shown that such conversion is possible, essentially with polynomial overhead, for the set of irrationals that are not Liouville numbers, and it is proved that any such number must be aLiouville number.