Let $ALL_{DFA} = \{(A) \mid A \text{ is a DFA and } L(A) = \Sigma^*\}$. Show that $ALL_{DFA}$ is decidable. Let B be the set of all infinite sequences over $\{0, 1, 2\}$. Show that B is uncountable, using a proof by diagonalization.
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To do this, we can construct a Turing machine that simulates the DFA on all possible inputs and checks if the DFA accepts all strings in D*. If the DFA accepts all strings in D*, the Turing machine accepts. Otherwise, it rejects. Since a DFA has a finite number Show more…
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