hw11soln - Inductive arguments Here’s question 9 on...

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Unformatted text preview: Inductive arguments Here’s question 9 on midterm 2: Let G be a context-free grammar in Chomsky normal form and S * ⇒ w be a derivation of w ∈ Σ * with a derivation tree T . Suppose the height of T is n . Prove that | w | ≤ 2 n- 1 . Some of you pointed out that derivation trees in Chomsky normal form are binary trees and this is a property of binary trees. I didn’t accept this answer. The fact that trees where each node has at most two children are binary trees should be completely obvious to any freshman CS major! It’s an unacceptable proof for an exam in a 300 level course. Instead, this is a straightforward inductive argument. If you don’t understand how to make clear inductive arguments, you will have difficulty passing this class (hint for the final). This skill is also extremely important to your success in a career as a computer scientist and/or programmer. Here’s how to prove this. Production rules in Chomsky normal form appear only as follows....
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hw11soln - Inductive arguments Here’s question 9 on...

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