Don't use that paper! I tried to use the parsing technique in that paper while working on a parser for use at the CME, and it caused me weeks of headaches.

First, you'll note the algorithm is extremely complicated--nothing like the simple top-down algorithm that makes PEGs so attractive. Not only is it complicated, it misses basic refactoring issues--some logic is duplicated across functions, and the functions interact in ugly ways.

Second, it doesn't even handle left recursion correctly. Throw a ruleset like this at their parser

A -> B "a"

B -> C "b"

C -> B / A / "c"

and it will explode into a million little pieces, because the authors did not account for any recursive rule having multiple recursion points. Don't even try something like

S -> A / B

A -> A "a" / B / a

B -> B "b" / A / "b"