The data set provided source code in C on how to compute Collatz dynamics by automata in terms of residue classes. It also includes algorithms implemented by C codes that can output residue classes by inputting reduced dynamics.  The formular for computing a residue class for a given reduced dynamics is as follows:

Function $Invrs(\cdot)$. 

$Invrs: c \rightarrow rs$ takes as input \\

$c=O$ or \\

$c=I^{p_1}O^{q_1}I^{p_2}O^{q_2}...I^{p_n}O^{q_n} \in \{I,O\}^{\geq 2},$ $p_i,q_i\in \mathbb{N}^*, i=1,2,...,n, n \in \mathbb{N}^*$\\