Answer

Correct Option: (i) $|Input|+1$

Explanation

Moore Machine: Output depends only on present state, and output is associated with state entry, including the initial state before any input is consumed.

• For input length $n$, the machine visits $n+1$ states: $q_0$ (initial, no input) $\xrightarrow{a_1} q_1 \xrightarrow{a_2} \dots \xrightarrow{a_n} q_n$.
• Each state produces one output symbol $\lambda(q_i)$.
• Hence output string length = $n+1$.

Mealy Machine contrast: Output depends on transition (state + input), so output length = $|Input|$ = $n$ (one per input symbol).

Given input 101010, $|Input|=6$ → Moore output length = $7$.

Final Answer

Moore machine output length is $|Input|+1$ → Option (i).