Palindrome

languages

Definition

Palindrome

A string is called palindrome iff:

where is the mirror image of .

Examples

Testing whether a language is regular

Let be a regular language. The following languages are defined from :

Then the task is to determine whether each is regular.

• is regular, because regular languages are closed under reversal.
• need not be regular, because the operation is not a closure property of regular languages.
• need not be regular, because the operation is not a closure property of regular languages.