Theory of Computation quizzes
What computers can solve, what they can’t, and how simple models help us understand the limits of computation.
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From Theory of Computation: Finite automata and regular languages · Deterministic Finite Automata
Why can no DFA recognize the language of strings aⁿbⁿ (n a's followed by n b's) for every n?
- Its alphabet cannot hold two letters
- It cannot reread earlier symbols
- It would need unboundedly many states
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Answer: It would need unboundedly many states
To match the b's it must remember how many a's it saw, and n can be any number, so no fixed finite set of states can store it.
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