I was wondering if there is a good bibliography of attempts to investigate the Collatz conjecture as a formal grammar? (or any other attempts in the CS community to deal with this class of generative phenomena & their "halting" properties).
$\begingroup$
$\endgroup$
3
-
$\begingroup$ as a sort of folklore approach, there is a fairly natural way to study this problem by building an FSM transducer that computes iterates in binary (least significant bit to most significant bit) although have not seen this in a paper. dont know if this construction is in the shallit and wilson paper, that may be the closest published paper to the transducer technique. $\endgroup$– vznJun 2, 2012 at 4:52
-
$\begingroup$ more on collatz conjecture from FSM transducer angle & misc refs $\endgroup$– vznSep 19, 2013 at 17:02
-
2$\begingroup$ See also this question and its answer. $\endgroup$– J.-E. PinNov 26, 2013 at 10:02
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
1
I guess these papers by Jeffrey C. Lagarias could help:
- The 3x+1 problem: An annotated bibliography (1963--1999) (sorted by author).
- The 3x+1 Problem: An Annotated Bibliography, II (2000-2009).
Another good source is the recent book "The Ultimate Challenge". In it chapter "Generalized $3x+1$ functions and the theory of computation",section $\#$ 8, can also be of interest.
answered Mar 26, 2011 at 21:52
-
$\begingroup$ thanks, I just wanted to see what else bubbles up before accepting the answer. $\endgroup$– DenizMar 28, 2011 at 1:44
$\begingroup$
$\endgroup$
0
Specifically, you may want to check out this paper by Shallit and Wilson: The "3x+1" Problem and Finite Automata", Bulletin of the EATCS, 46 (1992), pp. 182-185.
EDITED TO ADD: This appears as result 8.5 in the "section #8" part of Oleksandr Bondarenko's answer.
