Usually, a parser for an *LL*(*k*)-grammar *G* is a deterministic pushdown
transducer which produces a leftmost derivation for a given input string
.
Ukkonen (1983) has given a family of *LL*(2)-grammars
proving that every parser for these grammars has exponential size.
If we add to a parser the possibility to manipulate a constant number of
pointers which point to positions within the constructed part of the leftmost
derivation and to change the output in such positions, we obtain an extended
parser for the *LL*(*k*)-grammar *G*.
Given an arbitrary *LL*(*k*)-grammar *G*, we will show how to construct an
extended parser of polynomial size manipulating at most *k*^{2} pointers.