Look-ahead on pushdowns (Q579952)

The general notion of look-ahead on pushdowns is used to prove that (1) the deterministic iterated pushdown languages are closed under complementation, (2) the deterministic iterated pushdown languages are properly included in the nondeterministic iterated pushdown languages; the counter example is a very simple linear context-free language, independent of the amount of iteration, (3) LL(k) iterated indexed grammars can be parsed by deterministic iterated pushdown automata, and (4) it is decidable whether an iterated indexed grammar is LL(k). Analogous results hold for iterated pushdown automata with regular look- ahead on the input, and LL-regular iterated indexed grammars.