Collatz Automata and Compute Residue Class from Reduced Dynamics by Formular

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},$ $p_i,q_i\in \mathbb{N}^*, i=1,2,...,n, n \in \mathbb{N}^*$\\$CntO(c)=\lceil \log_21.5*CntI(c)\rceil,$ \\$CntO(s)<\lceil \log_21.5*CntI(s)\rceil, s=Substr(c,1,k), k=1,2,...,|c|-1,$ \\and outputs \\$rs=[0]_2$ when $c=O$, or\\$rs=([-\sum_{i=1}^nA_iB_iC_{i-1}]_{2^{|c|}} \cap \{x|x>\Psi*\frac{2^{\sum_{i=1}^n(p_i+q_i)}}{2^{\sum_{i=1}^n(p_i+q_i)}-3^{\sum_{i=1}^np_i}}\})$when $|c|\geq2,$ where $A_i=3^{p_i}-2^{p_i}$,$B_i=(3^{\sum_{j=1}^ip_j})^{-1} \mod C_n$,$C_i=2^{\sum_{j=1}^i(p_j+q_j)}, C_0=1,$\\$\Psi=\prod_{i=2}^na_ib_1+\prod_{i=3}^na_ib_2+...+\prod_{i=n-1}^na_ib_{n-2}+\prod_{i=n}^na_ib_{n-1}+b_n,$\\$a_i=\frac{3^{p_i}}{2^{p_i+q_i}},b_i=\frac{3^{p_i}-2^{p_i}}{2^{p_i+q_i}}.$