So... you want to tell whether or not a string is composed entirely of the alphabet a-z? That's pretty easy with a regexp.

if ($string =~ /^[a-z]+$/) {
    print "Valid\n";
} else {
    print "Invalid\n";
}
[download]

You mentioned finite automata in your subject line, though. Am I missing something else here? ;)

Cheers,
Paul