One of the following is a recursive definition of the set of bit strings that ar
ID: 3012174 • Letter: O
Question
One of the following is a recursive definition of the set of bit strings that are palindromes. There are two types of palindromes, so we need two base cases, namely lambda is a palindrome, and x is a palindrome for every symbol x. The recursive step is that if alpha is a palindrome and x is a symbol, then x alpha x is a palindrome. There is only one palindrome, so we need only one base case, namely lambda is a palindrome, and x is the only palindrome for every symbol x. The definition is impossible to be formed. There are two types of palindromes, so we need two base cases, namely lambda is a palindrome, and x is a palindrome for every symbol x. The recursive step is that if alpha is a palindrome and x is a symbol, then x alpha x is NOT a palindrome.Explanation / Answer
The empty string is a palindrome. All strings with one character are palindromes. All strings of the form cwc are palindromes, where c is a character and w is a palindrome.
hence option A) is correct
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