11.5: Activities
Develop an inductive definition of the set of words \(\Sigma^{\ast}\) from the alphabet \(\Sigma = \{ \text{a},\text{b},\text{c} \}\text{.}\)
Then verify that the word \(\text{ccababb}\) is in the set by tracing it back to the base clause.
- Hint.
-
Steps:
- Think of a simple way to form new words from old (inductive clause).
- Then think about the basic words you need to get the process started (base clause).
- Finally, decide whether you are certain you can form every possible word in a finite number steps starting at some base word.
Let \(\Sigma = \{\text{a},\text{z}\}\text{.}\) Write an inductive definition for the set of words in \(\Sigma^{\ast}\) that have the same number of \(\text{a}\) letters as \(\text{z}\) letters.