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). 
Collatz Conjecture & Grammars / Automata
fl.formal languages;nt.number theory;halting problem
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.