# Collatz Conjecture & Grammars / Automata

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).

• 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.
– vzn
Jun 2 '12 at 4:52
• more on collatz conjecture from FSM transducer angle & misc refs
– vzn
Sep 19 '13 at 17:02
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.