Practice Solving Recurrence Equations (13.5) - Counting Using Recurrence Equations

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6 sample questions

Question 1.
Define a recurrence equation.
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Look for terms that express future values based on past values.
Question 2.
What is S(1) for bit strings avoiding '00'?
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Consider all possible single digit strings.
3Question 3.
What defines a recurrence equation?
- An explicit formula
- A method to solve algebraic equations
- An equation relating terms of a sequence
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Think of it as a definition involving sequences.
4Question 4.
True or False: Recurrence relations can only have a single solution.
- True
- False
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Consider scenarios of supplying initial terms.
Question 5.
Prove that for any recurrence relation of the form T(n) = aT(n-1) + b, where a ≠ 0, you can derive a formula.
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Start with base cases and build upwards.
Question 6.
Demonstrate the uniqueness of solutions in a linear homogeneous recurrence relation when given initial conditions matching its degree.
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Reflect on how initial terms dictate the future terms.

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