Practice Comparison Of Set P With Π* (5.2.3) - Countability of the set of all strings over a finite alphabet

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6 sample questions

Question 1.
What is a finite alphabet?
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Think of letters of the English alphabet.
Question 2.
What is Π*?
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Consider how many ways you can combine letters.
3Question 3.
What does it mean for a set to be countable?
- It can be finite
- It can be listed with natural numbers
- It contains infinite elements
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Think about how you would list items.
4Question 4.
Is the set P (valid programs) countable?
- True
- False
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Remember the definition of valid programs.
Question 5.
Prove that the set of all possible strings from an alphabet {x, y, z} is countable.
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Start with the shortest strings and build up.
Question 6.
If you had an infinite number of valid programs, how would you ensure that each one can be included in your enumeration?
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Analyze the structure of valid programs.

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