Notes on computational linguistics.pdf - UCLA Department of ...

Stabler - Lx 185/209 2003
2.3 Finite state recognizers
(15) A subset of the context free grammars have rules that are only of the following forms, where word is a
lexical item and p,r are categories:
p :˜ [word,r].
p :˜ [].
These grammars “branch only on the right” – they are “right linear.”
(16) Right linear grammars are finite state in the following sense:
there is a finite bound k such that every sentence generated by a finite state grammar can be
recognized or rejected with a sequence (“stack”) in the “workspace” of length no greater than
k.
(17) Right linear grammars can be regarded as presentations of finite state transition graphs, where the
empty productions indicate the final states.
For example, the following grammar generates {0, 1} ∗ :
s :˜ [0,s].
s :˜ [1,s].
s :˜ [].
Another example
s :˜ [the,t].
t :˜ [cat,u].
u :˜ [is,v].
v :˜ [on,w].
w :˜ [the,x].
x :˜ [mat,y].
y :˜ [].
the
s t
cat
u
is
(18) These properties will be carefully established in standard texts on formal language theory and the theory
of computatation (Moll, Arbib, and Kfoury, 1988; Lewis and Papadimitriou, 1981; Hopcroft and Ullman,
1979; Salomaa, 1973), but the basic ideas here are simple.
Finite state grammars like this are sometimes used to represent the set of lexical sequences that most
closely fit with an acoustic input.
These grammars are also used to model parts of OT phonology (Ellison, 1994; Eisner, 1997; Frank and
Satta, 1998).
31
v
1
0
s
on
w
the
x
mat
y