CS 390 Solutions to Test I

1. T, F, T, T, F.

2(a)
(b)

3. Basis Step: If , then .

Induction: Assume that for an arbitrary string x.
Then for an arbitrary symbol b, by the definition of the length. By the induction hypothesis, , which is equal to . Hence .
On the other hand by the application of the definition of the length. Hence .

4. By noticing the two cycles at , is obtained.

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