And I show a paper that is V.Velichkov et al., The Additive Differential Probability of ARX.

I have a question in chapter 5.2.

V.Velichkov et al. said that "In general, following the mapping in Table 2, an initial state $$S[0]=j \in \{0,2,4,6\}$$ will match final states $$S[n-1]=j$$ and $$S[n-1]=j+1$$.

I want to know why this is correct.