Question: The construction in Theorem1.54 shows that everyGNFA is equivalent to aGNFA with only two states. We can show that an opposite phenomenon occurs for DFAs.

The construction in Theorem1.54 shows that everyGNFA is equivalent to aGNFA with only two states. We can show that an opposite phenomenon occurs for DFAs. Prove that for every k > 1, a language Ak ⊆ {0,1}^* exists that is recognized by a DFA with k states but not by one with only k − 1 states.

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