GIGs are based the idea of providing additional descriptive power to handle some canonical NLP problems, where LIGs fail. The canonical NLP problems which exceed context-free power are: multiple agreements, reduplication, and crossing dependencies [4]. We explain the problems in certain details in the following section to compare different formalisms towards NLP. Here, we give the definition of GIGs from [4]:
A GIG is a 6-tuple 
where N, T, I are
finite pairwise disjoint sets same as the LIG definition. 
is
the start stack symbol (not in I, N, T) and P is a finite set of
productions, having the following form:
or 
or 
or 
(push)
or 
(pop)
The derives relation 
on sentential forms are
defined as: Let 
and 
be in 
,
be in 
, x in I, w be in 
and 
in 
. Then,
is a production of
type (a.) (i.e., 
or 
)
then:
or 
is a production
of type (b.) (push), then:
is a production of
type (c.) (pop), then:
It has been showed that recognition of the language generated by a
GIG is in bounded polynomial time: 
. An algorithm to
construct an LR parsing table for global indexed language is
presented in [5], which also shows that it is a full
AFL. One thing needs to be pointed out is that global indexed
languages may contain languages not in indexed languages (MIX
language, Gazdar, 1988). We provide the case in Example
3 [4].
Example 3. (MIX language)
where P is: 
, 
, 
, 
,
, 
, 
, 
, 
, 
,
, 
,
The language generated by 
: 
and 
.
In comparing with LIGs, GIGs have provided more descriptive power on solving NLP problems. We illustrate this point in next section with examples.