Collatz Conjecture & Grammars / Automata
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.