It is true that the set of palindromes can not be matched with a regexp.

However, with Perl's extended regexps, it is possible. Indeed, this is in the Regexp::Common module.

perl -wne 'use Regexp::Common; /^$RE{lingua}{palindrome}$/ and print "
+palindrome\n";'
[download]

Update: beware, the above snippet only matches lines consisting of only letters.