Consider the following deterministic finite automaton (DFA). The number of strings of length 8 accepted by the above automaton is \(\underline{\hspace{2cm}}\).
Consider the following deterministic finite automaton (DFA). The number of strings of length 8 accepted by the above automaton is \(\underline{\hspace{2cm}}\).
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Correct Answer: 256
Solution and Explanation
Step 1: Observe the accepting state.
The DFA has a single accepting state with a self-loop on both input symbols \( 0 \) and \( 1 \).
Step 2: Reachability of accepting state.
From the start state, every string of length at least 2 can reach the accepting state, after which the automaton stays in the accepting state for all remaining symbols.
Step 3: Count binary strings of length 8.
Since all binary strings of length 8 are accepted:
\[ \text{Number of strings} = 2^8 = 256 \]
Final Answer: \[ \boxed{256} \]
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