as $\mathcal{C}^w$. In a similar way to AfAs, the automaton $ A $ reads $ {\mbox{\textcent}}w {\$}$ symbol by symbol from the left to the right and $ A $ operates on the classical configurations. Each such configuration, say $ (s,c) $, can be seen as the state of an affine system which we represent as $ {\langle s,c \rangle} $ (a vector in the standard basis of $ \mathbb{R}^N $). During the computation, similarly to quantum models, $ A $ can be in more than one classical configuration with some values, i.e. $$v =\sum_{(s,c) \in \mathcal{C}^w} \alpha_{s,c} {\langle s,c \rangle} \mbox{ satisfying that } \sum_{(s,c) \in \mathcal{C}^w} \alpha_{s,c} = 1.$$ Due to their simplicity, we use such linear combinations to trace the computation of an AfCA. Then we can also define the affine transition matrix $ M_\sigma $ for each $ \sigma \in \tilde{\Sigma} $ as follows: $$M_\sigma{\langle s,c \rangle} = \sum_{s'\in S, d\in \{-1, 0, +1\}} \delta(s, \sigma, \theta(c), s', d){\langle s',c+d \rangle},$$ where $ \theta(c) = Z$ if $ c = 0 $, and $ \theta(c) = NZ $ otherwise. At the beginning of computation, $A$ is in $ v_0 = {\langle s_I,0 \rangle} $. Then, after 