Automaton accepting $\{a^{2i}bc^{2k} \mid i, k \in\mathbb{N}\}$ How can I produce an automaton accepting $\{a^{2i}bc^{2k} \mid i, k \in\mathbb{N}\}$? I am essentially confused about exactly what the $2i$ and $2k$ mean. Does that mean that the automaton only accepts strings where the number of $a$'s and $b$'s are multiples of $2$ and there is one occurrence of $b$ between $a$ and $c$? Any help is greatly appreciated, thanks.
Yes, it means exactly that. $i$ and&nbsp;$k$ are arbitrary natural numbers, so $2i$ and&nbsp;$2k$ are arbitrary even natural numbers.