why top down parser cannot handle left recursion?

Question

I wanted to know why top down parsers cannot handle left recursion and we need to eliminate left recursion due to this as mentioned in dragon book..

Answer 1

Think of what it's doing. Suppose we have a left-recursive production rule A -> Aa | b, and right now we try to match that rule. So we're checking whether we can match an A here, but in order to do that, we must first check whether we can match an A here. That sounds impossible, and it mostly is. Using a recursive-descent parser, that obviously represents an infinite recursion.

It is possible using more advanced techniques that are still top-down, for example see [1] or [2].

[1]: Richard A. Frost and Rahmatullah Hafiz. A new top-down parsing algorithm to accommodate ambiguity and left recursion in polynomial time. SIGPLAN Notices, 41(5):46–54, 2006.
[2]: R. Frost, R. Hafiz, and P. Callaghan, Modular and efficient top-down parsing for ambiguous left-recursive grammars. ACL-IWPT, pp. 109 – 120, 2007.