Compacting the Penn Treebank Grammar 
Alexander Krotov and Mark Hepple and Robert Gaizauskas and Yorick Wilks 
Department of Computer Science, Sheffield University 
211 Portobello Street, Sheffield S1 4DP, UK {alexk, hepple, robertg, yorick}@dcs.shef.ac.uk 
Abstract 
Treebanks, such as the Penn Treebank (PTB), 
offer a simple approach to obtaining a broad 
coverage grammar: one can simply read the 
grammar off the parse trees in the treebank. 
While such a grammar is easy to obtain, a 
square-root rate of growth of the rule set with 
corpus size suggests that the derived grammar 
is far from complete and that much more tree- 
banked text would be required to obtain a com- 
plete grammar, if one exists at some limit. 
However, we offer an alternative explanation 
in terms of the underspecification of structures 
within the treebank. This hypothesis is ex- 
plored by applying an algorithm to compact 
the derived grammar by eliminating redund- 
ant rules - rules whose right hand sides can be 
parsed by other rules. The size of the result- 
ing compacted grammar, which is significantly 
less than that of the full treebank grammar, is 
shown to approach a limit. However, such a 
compacted grammar does not yield very good 
performance figures. A version of the compac- 
tion algorithm taking rule probabilities into ac- 
count is proposed, which is argued to be more 
linguistically motivated. Combined with simple 
thresholding, this method can be used to give 
a 58% reduction in grammar size without signi- 
ficant change in parsing performance, and can 
produce a 69% reduction with some gain in re- 
call, but a loss in precision. 
1 Introduction 
The Penn Treebank (PTB) (Marcus et al., 1994) 
has been used for a rather simple approach 
to deriving large grammars automatically: one 
where the grammar rules are simply 'read off' 
the parse trees in the corpus, with each local 
subtree providing the left and right hand sides 
of a rule. Charniak (Charniak, 1996) reports 
precision and recall figures of around 80% for 
a parser employing such a grammar. In this 
paper we show that the huge size of such a tree- 
bank grammar (see below) can be reduced in 
size without appreciable loss in performance, 
and, in fact, an improvement in recall can be 
achieved. 
Our approach can be generalised in terms 
of Data-Oriented Parsing (DOP) methods (see 
(Bonnema et al., 1997)) with the tree depth of 
1. However, the number of trees produced with 
a general DOP method is so large that Bonnema 
(Bonnema et al., 1997) has to resort to restrict- 
ing the tree depth, using a very domain-specific 
corpus such as ATIS or OVIS, and parsing very 
short sentences of average length 4.74 words. 
Our compaction algorithm can be easily exten- 
ded for the use within the DOP framework but, 
because of the huge size of the derived grammar 
(see below), we chose to use the simplest PCFG 
framework for our experiments. 
We are concerned with the nature of the rule 
set extracted, and how it can be improved, with 
regard both to linguistic criteria and processing 
efficiency. Inwhat follows, we report the worry- 
ing observation that the growth of the rule set 
continues at a square root rate throughout pro- 
cessing of the entire treebank (suggesting, per- 
haps that the rule set is far from complete). Our 
results are similar to those reported in (Krotov 
et al., 1994). 1 We discuss an alternative pos- 
sible source of this rule growth phenomenon, 
partial bracketting, and suggest that it can be 
alleviated by compaction, where rules that are 
redundant (in a sense to be defined) are elimin- 
ated from the grammar. 
Our experiments on compacting a PTB tree- 
1 For the complete investigation of the grammar ex- 
tracted from the Penn Treebank II see (Gaizauskas, 1995) 
699 
20000 
15000 
i0000 
5000 
0 
0 20 40 60 80 i00 
Percentage of the corpus 
Figure 1: Rule Set Growth for Penn Treebank 
II 
bank grammar resulted in two major findings: 
one, that the grammar can be compacted to 
about 7% of its original size, and the rule num- 
ber growth of the compacted grammar stops at 
some point. The other is that a 58% reduction 
can be achieved with no loss in parsing perform- 
ance, whereas a 69% reduction yields a gain in 
recall, but a loss in precision. 
This, we believe, gives further support to 
the utility of treebank grammars and to the 
compaction method. For example, compaction 
methods can be applied within the DOP frame- 
work to reduce the number of trees. Also, by 
partially lexicalising the rule extraction process 
(i.e., by using some more frequent words as well 
as the part-of-speech tags), we may be able to 
achieve parsing performance similar to the best 
results in the field obtained in (Collins, 1996). 
2 Growth of the Rule Set 
One could investigate whether there is a fi- 
nite grammar that should account for any text 
within a class of related texts (i.e. a domain 
oriented sub-grammar of English). If there is, 
the number of extracted rules will approach a 
limit as more sentences are processed, i.e. as 
the rule number approaches the size of such an 
underlying and finite grammar. 
We had hoped that some approach to a limit 
would be seen using PTB II (Marcus et al., 
1994), which larger and more consistent for 
bracketting than PTB I. As shown in Figure 1, 
however, the rule number growth continues un- 
abated even after more than 1 million part-of- 
speech tokens have been processed. 
3 Rule Growth and Partial 
Bracketting 
Why should the set of rules continue to grow in 
this way? Putting aside the possibility that nat- 
ural languages do not have finite rule sets, we 
can think of two possible answers. First, it may 
be that the full "underlying grammar" is much 
larger than the rule set that has so far been 
produced, requiring a much larger tree-banked 
corpus than is now available for its extrac- 
tion. If this were true, then the outlook would 
be bleak for achieving near-complete grammars 
from treebanks, given the resource demands of 
producing hand-parsed text. However, the rad- 
ical incompleteness of grammar that this al- 
ternative implies seems incompatible with the 
promising parsing results that Charniak reports 
(Charniak, 1996). 
A second answer is suggested by the presence 
in the extracted grammar of rules such as (1). 2 
This rule is suspicious from a linguistic point of 
view, and we would expect that the text from 
which it has been extracted should more prop- 
erly have been analysed using rules (2,3), i.e. as 
a coordination of two simpler NPs. 
NP --~ DT NN CC DT NN (1) 
NP --~ NP CC NP (2) 
gP --+ DT NN (3) 
Our suspicion is that this example reflects a 
widespread phenomenon of partial bracketting 
within the PTB. Such partial bracketting will 
arise during the hand-parsing of texts, with (hu- 
man) parsers adding brackets where they are 
confident that some string forms a given con- 
stituent, but leaving out many brackets where 
they are less confident of the constituent struc- 
ture of the text. This will mean that many 
rules extracted from the corpus will be 'flat- 
ter' than they should be, corresponding prop- 
erly to what should be the result of using sev- 
eral grammar rules, showing only the top node 
and leaf nodes of some unspecified tree structure 
(where the 'leaf nodes' here are category sym- 
bols, which may be nonterminal). For the ex- 
ample above, a tree structure that should prop- 
erly have been given as (4), has instead received 
2PTB POS tags are used here, i.e. DT for determiner, 
CC for coordinating conjunction (e.g 'and'), NN for noun 
700 
only the partial analysis (5), from the flatter 
'partial-structure' rule (1). 
i. NP 
NP CC NP 
DT NN DT NN 
(4) 
ii. NP (5) 
DT NN CC DT NN 
4 Grammar Compaction 
The idea of partiality of structure in treebanks 
and their grammars suggests a route by which 
treebank grammars may be reduced in size, or 
compacted as we shall call it, by the elimination 
of partial-structure rules. A rule that may be 
eliminable as a partial-structure rule is one that 
can be 'parsed' (in the familiar sense of context- 
free parsing) using other rules of the grammar. 
For example, the rule (1) can be parsed us- 
ing the rules (2,3), as the structure (4) demon- 
strates. Note that, although a partial-structure 
rule should be parsable using other rules, it does 
not follow that every rule which is so parsable 
is a partial-structure rule that should be elimin- 
ated. There may be defensible rules which can 
be parsed. This is a topic to which we will re- 
turn at the end of the paper (Sec. 6). For most 
of what follows, however, we take the simpler 
path of assuming that the parsability of a rule 
is not only necessary, but also sufficient, for its 
elimination. 
Rules which can be parsed using other rules 
in the grammar are redundant in the sense that 
eliminating such a rule will never have the ef- 
fect of making a sentence unparsable that could 
previously be parsed. 3 
The algorithm we use for compacting a gram- 
mar is straightforward. A loop is followed 
whereby each rule R in the grammar is ad- 
dressed in turn. If R can be parsed using other 
rules (which have not already been eliminated) 
then R is deleted (and the grammar without R 
is used for parsing further rules). Otherwise R 
3Thus, wherever a sentence has a parse P that em- 
ploys the parsable rule R, it also has a further parse that 
is just like P except that any use of R is replaced by a 
more complex substructure, i.e. a parse of R. 
is kept in the grammar. The rules that remain 
when all rules have been checked constitute the 
compacted grammar. 
An interesting question is whether the result 
of compaction is independent of the order in 
which the rules are addressed. In general, this is 
not the case, as is shown by the following rules, 
of which (8) and (9) can each be used to parse 
the other, so that whichever is addressed first 
will be eliminated, whilst the other will remain. 
B --+ C (6) 
C --+ B (7) 
A -+ B B (8) 
A -~ C C (9) 
Order-independence can be shown to hold for 
grammars that contain no unary or epsilon 
('empty') rules, i.e. rules whose righthand sides 
have one or zero elements. The grammar that 
we have extracted from PTB II, and which is 
used in the compaction experiments reported in 
the next section, is one that excludes such rules. 
For further discussion, and for the proof of the 
order independence see (Krotov, 1998). Unary 
and sister rules were collapsed with the sister 
nodes, e.g. the structure (S (NP -NULL-) (VP 
VB (NP (QP ...))) .) will produce the fol- 
lowing rules: S -> VP., VP -> VB QPand QP 
_> . 4 
° ,. 
5 Experiments 
We conducted a number of compaction exper- 
iments: 5 first, the complete grammar was 
parsed as described in Section 4. Results ex- 
ceeded our expectations: the set of 17,529 rules 
reduced to only 1,667 rules, a better than 90% 
reduction. 
To investigate in more detail how the com- 
pacted grammar grows, we conducted a third 
experiment involving a staged compaction of the 
grammar. Firstly, the corpus was split into 10% 
chunks (by number of files) and the rule sets 
extracted from each. The staged compaction 
proceeded as follows: the rule set of the first 
10% was compacted, and then the rules for the 
4See (Gaizauskas, 1995) for discussion. 
SFor these experiments, we used two parsers: Stol- 
cke's BOOGIE (Stolcke, 1995) and Sekine's Apple Pie 
Parser (Sekine and Grishman, 1995). 
701 
$ 
2 
2000 
1500 
I000 
500 
0 
: i 
0 20 40 60 80 i00 
Percentage of the corpus 
Figure 2: Compacted Grammar Size 
next 10% added and the resulting set again com- 
pacted, and then the rules for the next 10% ad- 
ded, and so on. Results of this experiment are 
shown in Figure 2. 
At 50% of the corpus processed the com- 
pacted grammar size actually exceeds the level 
it reaches at 100%, and then the overall gram- 
mar size starts to go down as well as up. This 
reflects the fact that new rules are either re- 
dundant, or make "old" rules redundant, so that 
the compacted grammar size seems to approach 
a limit. 
6 Retaining Linguistically Valid 
Rules 
Even though parsable rules are redundant in 
the sense that has been defined above, it does 
not follow that they should always be removed. 
In particular, there are times where the flatter 
structure allowed by some rule may be more lin- 
guistically correct, rather than simple a case of 
partial bracketting. Consider, for example, the 
(linguistically plausible) rules (10,11,12). Rules 
(11) and (12) can be used to parse (10), but 
it should not be eliminated, as there are cases 
where the flatter structure it allows is more lin- 
guistically correct. 
VP ~ VB NP PP 
VP ~ VB NP 
NP ~ NP PP 
i. VP ii. VP 
VB NP VB NP PP 
NP PP 
(10) 
(ii) 
(12) 
(13) 
We believe that a solution to this problem 
can be found by exploiting the date provided by 
the corpus. Frequency of occurrence data for 
rules which have been collected from the cor- 
pus and used to assign probabilities to rules, 
and hence to the structures they allow, so as 
to produce a probabilistic context-free grammar 
for the rules. Where a parsable rule is correct 
rather than merely partially bracketted, we then 
expect this fact to be reflected in rule and parse 
probabilities (reflecting the occurrence data of 
the corpus), which can be used to decide when 
a rule that may be eliminated should be elimin- 
ated. In particular, a rule should be eliminated 
only when the more complex structure allowed 
by other rules is more probable than the simpler 
structure that the rule itself allows. 
We developed a linguistic compaction al- 
gorithm employing the ideas just described. 
However, we cannot present it here due to 
the space limitations. The preliminary results 
of our experiments are presented in Table 1. 
Simple thresholding (removing rules that only 
occur once) was also to achieve the maximum 
compaction ratio. For labelled as well as unla- 
belled evaluation of the resulting parse trees we 
used the evalb software by Satoshi Sekine. See 
(Krotov, 1998) for the complete presentation of 
our methodology and results. 
As one can see, the fully compacted grammar 
yields poor recall and precision figures. This 
can be because collapsing of the rules often pro- 
duces too much substructure (hence lower pre- 
cision figures) and also because many longer 
rules in fact encode valid linguistic information. 
However, linguistic compaction combined with 
simple thresholding achieves a 58% reduction 
without any loss in performance, and 69% re- 
duction even yields higher recall. 
7 Conclusions 
We see the principal results of our work to be 
the following: 
* the result showing continued square-root 
growth in the rule set extracted from the 
PTB II; 
• the analysis of the source of this continued 
growth in terms of partial bracketting and 
the justification this provides for compac- 
tion via rule-parsing; 
• the result that the compacted rule set 
does approach a limit at some point dur- 
702 
Full Simply thresholded Fully compacted Linguistically compacted 
Grammar 1 Grammar 2 
Recall 70.55% 
Precision 77.89% 
Recall 73.49% 
Precision 81.44% 
Grammar size 15,421 
reduction (as % of full) 0% 
Labelled evaluation 
70.78% 30.93% 71.55% 70.76% 
77.66% 19.18% 72.19% 77.21% 
Unlabelled evaluation 
73.71% 43.61% 
80.87% 27.04% 
7,278 1,122 
53% 93% 
74.72% 73.67% 
75.39% 80.39% 
4,820 6,417 
69% 58% 
Table 1: Preliminary results of evaluating the grammar compaction method 
ing staged rule extraction and compaction, 
after a sufficient amount of input has been 
processed; 
• that, though the fully compacted grammar 
produces lower parsing performance than 
the extracted grammar, a 58% reduction 
(without loss) can still be achieved by us- 
ing linguistic compaction, and 69% reduc- 
tion yields a gain in recall, but a loss in 
precision. 
The latter result in particular provides further 
support for the possible future utility of the 
compaction algorithm. Our method is similar 
to that used by Shirai (Shirai et al., 1995), but 
the principal differences are as follows. First, 
their algorithm does not employ full context- 
free parsing in determining the redundancy of 
rules, considering instead only direct composi- 
tion of the rules (so that only parses of depth 
2 are addressed). We proved that the result of 
compaction is independent of the order in which 
the rules in the grammar are parsed in those 
cases involving 'mutual parsability' (discussed 
in Section 4), but Shirai's algorithm will elimin- 
ate both rules so that coverage is lost. Secondly, 
it is not clear that compaction will work in the 
same way for English as it did for Japanese. 

References 
Remko Bonnema, Rens Bod, and Remko Scha. 1997. 
A DOP model for semantic interpretation. In 
Proceedings of European Chapter of the ACL, 
pages 159-167. 
Eugene Charniak. 1996. Tree-bank grammars. In 
Proceedings of the Thirteenth National Confer- 
ence on Artificial Intelligence (AAAI-96), pages 
1031-1036. MIT Press, August. 
Michael Collins. 1996. A new statistical parser 
based on bigram lexical dependencies. In Proceed- 
ings of the 3~th Annual Meeting of the ACL. 
Robert Gaizauskas. 1995. Investigations into the 
grammar underlying the Penn Treebank II. Re- 
search Memorandum CS-95-25, University of 
Sheffield. 
Alexander Krotov, Robert Gaizauskas, and Yorick 
Wilks. 1994. Acquiring a stochastic context-free 
grammar from the Penn Treebank. In Proceedings 
of Third Conference on the Cognitive Science of 
Natural Language Processing, pages 79-86, Dub- 
lin. 
Alexander Krotov. 1998. Notes on compacting 
the Penn Treebank grammar. Technical Memo, 
Department of Computer Science, University of 
Sheffield. 
M. Marcus, G. Kim, M.A. Marcinkiewicz, 
R. MacIntyre, A. Bies, M. Ferguson, K. Katz, 
and B. Schasberger. 1994. The Penn Tree- 
bank: Annotating predicate argument structure. 
In Proceedings of ARPA Speech and Natural 
language workshop. 
Satoshi Sekine and Ralph Grishman. 1995. A 
corpus-based probabilistic grammar with only two 
non-terminals. In Proceedings of Fourth Interna- 
tional Workshop on Parsing Technologies. 
Kiyoaki Shirai, Takenobu Tokunaga, and Hozumi 
Tanaka. 1995. Automatic extraction of Japanese 
grammar from a bracketed corpus. In Proceedings 
of Natural Language Processing Pacific Rim Sym- 
posium, Korea, December. 
Andreas Stolcke. 1995. An efficient probabilistic 
context-free parsing algorithm that computes 
prefix probabilities. Computational Linguistics, 
21(2):165-201. 
