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I have this confusion related to palindrome language. I have found it being mentioned if a language L is equal to its reverse, it is a palindrome language.

But lets say

L = {aaab, baaa}

Then $L^R= \{baaa,aaab\}$


L = $L^R$ in this case

But the language isn't palindrome isn't it. Any insights?

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Why isn't it? Do you just mean that each word is not a palindrome? – Thomas Andrews Sep 13 '12 at 20:42
If so, it just depends on the definition of a language being palindromic. The definition you have is not the same as saying every word in $L$ is a palindrome, – Thomas Andrews Sep 13 '12 at 20:43

"Palindrome language" is not a technical term that has a generally accepted meaning. Just from the words one could imagine several different meanings for it:

  • The language consisting of all palindromes over some given alphabet.
  • A language whose members are always palindromes (but not necessarily all the palindromes).
  • A language that is closed under the operation of reversing a word (that's the one you have got there).

Neither of theses definitions are, however, one that an unprepared reader can be expected to understand. But fear not! That is what definitions are for.

One can make "palindrome language" into a technical term for the duration of a book, an article, an exercise, simply by setting forth a definition that declares what it will mean. The definition can be one of the three suggested above, or something fourth and different ... so long as it defines something that you need to have a name for for your purposes.

So, if you're reading an exercise that defines a palindrome language to be an $L$ such that $L=L^R$ (which seems to be the most relevant use of the term in the first page of Google hits), then that's what "palindrome language" means for the purpose of doing that exercise. It's not as if any of the possible meanings is something that crops often enough to warrant attaching a name to it permanently.

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its a word that is pronounced the same when you say it backwards. EXAMPLE: mom, say it backwards, it still says,mom. did, say it backwards, its still did.

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