I have a homework problem that I'm working through:
$L = {ww^R : w \in \{a,b\}^+}$
So I get the following:
$S \to aSa | bSb | \Lambda$
I am confused about the $\{a, b\}^+$, doesn't this mean that our alphabet cannot include $\Lambda$? If so, how do we terminate?
I believe that you are mixing two terms: "alphabet" and "language". The alphabet is the underlying set of symbols ("letters"); the language is the set of all words formed with symbols from the alphabet ("vocabulary"). As such, $\Lambda$ is never an element of the alphabet, because it is not supposed to be a letter; it is supposed to be a word, therefore it must belong to the vocabulary, i.e. it is a result of the application of production rules in the grammar. (Your question is like wondering why "abba" is not a member of the alphabet; because it is a word, not a letter.)