Question: Consider the language A2 ? {0, 1}? defined as A2 = { w | there is a position i in w such that the symbol

Consider the language A2 ? {0, 1}? defined as

A2 = { w | there is a position i in w such that the symbol at position i (in w) is 0, and the symbol at position i + 2 is 1. }

Prove that any DFA recognizing A2 has at least 5 states.

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