Classes of Szilard Languages in NC^1

We prove that Szilard languages of context-free grammars can be accepted by an indexing alternating Turing machine (indexing ATM) in logarithmic time and space. The same result holds for leftmost Szilard languages of unrestricted (phrase-structure or type 0) grammars. Since the class of languages recognizable by an indexing ATM in logarithmic time equals the U
_E
-uniform NC
¹
class, we obtain that the above classes of Szilard languages are in NC
¹
. The inclusions are strict, since there exist languages in NC
¹
that cannot be Szilard languages of any context-free or unrestricted grammar.