Fig. 2

DFA intersection product. We represent the resulting intersection product of the at least one hit DFA for the seed \(\pi = \text {101}\) (top horizontal automaton), with the \(\text {1}\)-counting DFA (left vertical automaton). The dashed transitions represent ellipsis in the construction between \(m=2\) and \(m=\ell -1\), while the dotted transitions at the bottom of the resulting automaton make it complete