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

Stabler - Lx 185/209 2003
(50) Nem
not
fogok haza-menni kezdeni akarni V1 M V4 V3 V2
will-1s begin-inf want-inf home-go-inf
One analysis of verbal clusters in Hungarian (Koopman and Szabolcsi, 2000a) suggests that they “roll up” from
the end of the string as shown below:
rolling up:
Nem fogok akarni kezdeni haza−menni V1 V2 V3 M V4
not will−1s want−inf begin−inf home−go−inf
Nem fogok akarni haza−menni kezdeni V1 V2 M V4 V3
Nem fogok haza−menni kezdeni akarni V1 M V4 V3V2
[M] moves around V4, then [M V4] rolls up around V3, then [M V4 V3] rolls up around V2,…It turns out that
this kind of derivation can derive complex patterns of dependencies which can yield formal languages like
{a n b n c n | n ≥ 0}, oreven{a n b n c n d n e n | n ≥ 0} – any number of counting dependencies. We can define these
languages without any kind of “rolling up” constituents if we help ourselves to (unboundedly many) feature
values and unification:
% anbncn.pl
’S’ :˜ [’A’(X),’B’(X),’C’(X)].
’A’(s(X)) :˜ [a,’A’(X)]. ’B’(s(X)) :˜ [b,’B’(X)]. ’C’(s(X)) :˜ [c,’C’(X)].
’A’(0) :˜ []. ’B’(0) :˜ []. ’C’(0) :˜ [].
4.2 Semilinearity and some inhuman linguistic patterns
In the previous section we saw grammars for {a n b n | n ≥ 0}, {xx| x ∈{a, b} ∗ },and{a n b n c n | n ≥ 0}. These
languages all have a basic property in common, which can be seen by counting the number of symbols in each
string of each language.
For example,
{a n b n | n ≥ 0} ={ɛ,ab,aabb,aaabbb,...}
,wecanuse(x, y) to represent x a’s and y’bs, so we see that the strings in this language have the following
counts:
{(0, 0), (1, 1), (2, 2),...}={(x, y)| x = y}.
For {xx| x ∈{a, b} ∗ },wehaveallpairsN × N. For{a n b n c n | n ≥ 0} we have the set of triples {(x,y,z)| x =
y = z}. If we look at just the number of a’s in each language, considering the set of values of first coordinates
of the tuples, then we can list those sets by value, obtaining in all three cases the sequence:
0, 1, 2, 3,...
The patterns of dependencies we looked at above will not always give us the sequence 0, 1, 2, 3,..., though.
For example, the language
{(ab) n (ba) n | n ≥ 0} ={ɛ, abba, ababbaba, . . .}
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