consider \"alphabet\" consisting of the two letters a and b , together with the
ID: 3075861 • Letter: C
Question
consider "alphabet" consisting of the two letters a and b , together with the following rules for creating new "words" from old ones. The rules may be applied in any order. Use one rule at a time to create new words from old ones. RULE 1: Double the current word . ( for example, if bba is a word, then bbabba is a word.) RULE 2: Erase bb from the current word. ( for example babba is a word, then baa is a word.) RULE 3: Replace aaa in the current word by b. (for example, if aaaba is a word, then bba is a word ) RULE 4: If the last letter of the current word is a, then b at the right end of the current word. ( For example, if aba is a word, then abab is a word )b) list all of the words for which one application of one of the rules would result in the word bab
Explanation / Answer
We'll try undoing each rule to see the possible words that could be formed. You can't have just done rule 1, since bab isn't double another word. If you just did rule 2, you could have had bb in any location in the word, giving the possibilities of: bbbab and babbb If you just did rule 3, then you would have had aaa in the place of one of the b's, giving possibilities of: aaaab and baaaa If you just did rule 4, then you must have come from: ba So to recap, there are 5 possibilities of words you could have come from, and they are bbbab, babbb, aaaab, baaaa, and ba.
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