Is the set of LL(*) grammars the same as the set of CFG grammars?
Static LL(*) grammar analysis is undecidable. In other words, there are some grammars that are LL(*) but we can't figure this out statically. ANTLR v3 fails over to backtracking in this case and therefore can exhibit the PEG A->a/ab problem where ab is dead code in the cases where grammar analysis failed.

In ANTLR v4, I'm introducing adaptive LL(*), which does all grammar analysis at runtime. Because I have an actual input stream in my paw, I can discover every LL(*) decision. I'm also including full LL context (vs Strong LL == SLL context which is weaker). Because I also rewrite all immediate left recursion on-the-fly, ANTLR v4 handles all CFG except for indirect left recursive ones. These are much less common than the immediate left recursive ones like expressions.

e : e '*' e
  | e '+' e
  | INT
  ;


This works fine in v4.  operator precedence is assumed to go from highest to lowest for ambiguous alternatives.