Question: 4. Student: Why do we define deterministic finite automata using a set of final states? Wouldn't one final state suffice? Automata salesman: We uscd to

4. Student: "Why do we define deterministic finite automata using a

4. Student: "Why do we define deterministic finite automata using a set of final states? Wouldn't one final state suffice?" Automata salesman: "We uscd to make thcm that way, but we found that they aren't as powerful as our current model." Justify the salesman's answer, by exhibiting a regular language L that cannot be accepted by any DFA with one final state. Hint: it is enough to consider finite L 02

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