Off-line Optimization for Earley-style HPSG Processing 
Guido Minnen, Dale Gerdemann~ Thilo GStz * 
Sonderforschungsbereich 340 
University of Tfibingen 
Wilhelmstr. 113 
72074-Tfibingen 
Germany 
E-mail: minnen@sfs.nphil.uni-t uebingen.de 
Abstract 
A novel approach to HPSG based natural 
language processing is described that uses 
an off-line compiler to automatically prime 
a declarative grammar for generation or 
parsing, and inputs the primed grammar to 
an advanced Earley-style processor. This 
way we provide an elegant solution to the 
problems with empty heads and efficient 
bidirectional processing which is illustrated 
for the special case of HPSG generation. Ex- 
tensive testing with a large HPSG grammar 
revealed some important constraints on the 
form of the grammar. 
1 Introduction 
Bidirectionality of grammar is a research topic in 
natural language processing that is enjoying increas- 
ing attention (Strzalkowski, 1993a). This is mainly 
due to the clear theoretical and practical advantages 
of bidirectional grammar use (see, among others, 
Appelt, 1987). We address this topic in describing 
a novel approach to HPSG (Pollard and Sag, 1994) 
based language processing that uses an off-line com- 
piler to automatically prime a declarative grammar 
for generation or parsing, and hands the primed 
grammar to an advanced Earley processor. The de- 
veloped techniques are direction independent in the 
sense that they can be used for both generation and 
parsing with HPSG grammars. In this paper, we fo- 
cus on the application of the developed techniques 
in the context of the comparatively neglected area 
of HPSG generation. 
Shieber (1988) gave the first use of Earley's al- 
gorithm for generation, but this algorithm does not 
*The presented research was sponsored by 'l~eilpro - 
jekt B4 "Constraints on Grammar for Efficient Genera- 
tion" of the Sonderforschungsbereich 340 "Sprachtheo- 
retische Grundlagen fiir die Computerllnguistik" of the 
Deutsche Forschungsgemeinschaft. The authors wish to 
thank Paul King, Detmar Meurers and Shuly Wintner 
for valuable comments and discussion. Of course, the 
authors are responsible for all remaining errors. 
use the prediction step to restrict feature instantia- 
tions on the predicted phrases, and thus lacks goal- 
directedness. Though Gerdemann (1991) showed 
how to modify the restriction function to make top- 
down information available for the bottom-up com- 
pletion step, Earley generation with top-down pre- 
diction still has a problem in that generating the sub- 
parts of a construction in the wrong order might lead 
to massive nondeterminacy or even nontermination. 
Gerdemann (1991) partly overcame this problem by 
incorpQrating a head-driven strategy into Earley's 
algorithm. However, evaluating the head of a con- 
struction prior to its dependent subparts still suffers 
from efficiency problems when the head of a con- 
struction is either missing, displaced or underspec- 
ified. Furthermore, Martinovid and Strzalkowski 
(1992) and others have observed that a simple head- 
first reordering of the grammar rules may still make 
insufficient restricting information available for gen- 
eration unless the form of the grammar is restricted 
to unary or binary rules. 
Strzalkowski's Essential Arguments Approach 
(Ehh; 1993b) is a top-down approach to generation 
and parsing with logic grammars that uses off-line 
compilation to automatically invert parser-oriented 
logic grammars. The inversion process consists of 
both the automatic static reordering of nodes in 
the grammar, and the interchanging of arguments in 
rules with recursively defined heads. It is based on 
the notion of essential arguments, arguments which 
must be instantiated to ensure the efficient and ter- 
minating execution of a node. Minnen et al. (1995) 
observe that the EAA is computationally infeasible, 
because it demands the investigation of almost all 
possible permutations of a grammar. Moreover, 
the interchanging of arguments in recursive proce- 
dures as proposed by Strzalkowski fails to guarantee 
that input and output grammars are semantically 
equivalent. The Direct Inversion Approach (DI,~) of 
Minnen et al. (1995) overcomes these problems by 
making the reordering process more goal-directed 
and developing a reformulation technique that al- 
lows the successful treatment of rules which exhibit 
head-recursion. Both the EAA and the DIA were 
173 
presented as approaches to the inversion of parser- 
oriented grammars into grammars suitable for gen- 
eration. However, both approaches can just as well 
take a declarative grammar specification as input to 
produce generator and/or parser-oriented grammars 
as in Dymetman et al. (1990). In this paper we 
adopt the latter theoretically more interesting per- 
spective. 
We developed a compiler for off-line optimization 
of phrase structure rule-based typed feature struc- 
ture grammars which generalizes the techniques de- 
veloped in the context of the DIA, and we advanced 
a typed extension of the Earley-style generator of 
Gerdemann (1991). Off-line compilation (section 3) 
is used to produce grammars for the Earley-style 
generator (section 2). We show that our use of off- 
line grammar optimization overcomes problems with 
empty or displaced heads. The developed techniques 
are extensively tested with a large HPSG grammar for 
partial vP topicallzation in German (iiinrichs et al., 
1994). This uncovered some important constraints 
on the form of the phrase structure rules (phrase 
structure rules) in a grammar imposed by the com- 
piler (section 4). 
2 Advanced Earley Generation 
As Shieber (1988) noted, the main shortcoming of 
Earley generation is a lack of goal-directedness that 
results in a proliferation of edges. Gerdemann (1991) 
tackled this shortcoming by modifying the restric- 
tion function to make top-down information avail- 
able for the bottom-up completion step. Gerde- 
mann's generator follows a head-driven strategy in 
order to avoid inefficient evaluation orders. More 
specifically, the head of the right-hand side of each 
grammar rule is distinguished, and distinguished 
categories are scanned or predicted upon first. The 
resulting evaluation strategy is similar to that of the 
head-corner approach (Shieber et al., 1990; Gerde- 
mann and IIinrichs, in press): prediction follows 
the main flow of semantic information until a lex- 
ical pivot is reached, and only then are the head- 
dependent subparts of the construction built up in 
a bottom-up fashion. This mixture of top-down and 
bottom-up information flow is crucial since the top- 
down semantic information from the goal category 
must be integrated with the bottom-up subcatego- 
rization information from the lexicon. A strict top- 
down evaluation strategy suffers from what may be 
called head-recursion, i.e. the generation analog of 
left recursion in parsing. Shieber et al. (1990) show 
that a top-down evaluation strategy will fail for rules 
such as vP --* vp x, irrespective of the order of eval- 
uation of the right-hand side categories in the rule. 
By combining the off-line optimization process with 
a mixed bottom-up/top-down evaluation strategy, 
we can refrain from a complete reformulation of the 
grammar as, for example, in Minnen et al. (1995). 
2.1 Optimizations 
We further improved a typed extension of Gerde- 
mann's Earley generator with a number of tech- 
niques that reduce the number of edges created dur- 
ing generation. Three optimizations were especially 
helpful. The first supplies each edge in the chart 
with two indices, a backward index pointing to the 
state in the chart that the edge is predicted from, 
and a forward index poinfing to the states that are 
predicted from the edge. By matching forward and 
backward indices, the edges that must be combined 
for completion can be located faster. This index- 
ing technique, as illustrated below, improves upon 
the more complex indices in Gerdemann (1991) and 
is closely related to OLDT-resolution (Tamaki and 
Sato, 1986). 
1) active(Xo---~Xl*X2,1~2~ 
2) active(X:--~.Y1Y2,~3)) 
3) active(X2---*Y1.Y2, i,y 
4) passive(X2 --+ Y1 I/2 o, 2) 
Active edge 2 resulted from active edge 1 through 
prediction. The backward index of edge 2 is there- 
fore identified with the forward index of edge 1. 
Completion of an active edge results in an edge with 
identical backward index. In the case of our exam- 
ple, this would be the steps from edge 2 to edge 3 
and edge 3 to edge 4. As nothing gets predicted 
from a passive edge (4), it does not have a forward 
index. In order to use passive edge 4 for completion 
of an active edge, we only need to consider those 
edges which have a forward index identical to the 
backward index of 4. 
The second optimization creates a table of the cat- 
egories which have been used to make predictions 
from. As discussed in Gerdemann (1991), such a ta- 
ble can be used to avoid redundant predictions with- 
out a full and expensive subsumption test. The third 
indexes lexical entries which is necessary to obtain 
constant-time lexical access. 
The optimizations of our Earley-generator lead 
to significant gains in efficiency. However, despite 
these heuristic improvements, the problem of goal- 
directedness is not solved. 
2.2 Empty Heads 
Empty or displaced heads present the principal goal- 
directedness problem for any head-driven generation 
approach (Shieber et al., 1990; K6nig, 1994; Gerde- 
mann and IIinrichs, in press), where empty head 
refers not just to a construction in which the head 
has an empty phonology, but to any construction 
in which the head is partially unspecified. Since 
174 
phonology does not guide generation, the phonologi- 
cal realization of the head of a construction plays no 
part in the generation of that construction. To bet- 
ter illustrate the problem that underspecified heads 
pose, consider the sentence: 
Hal Karl Marie geki~'flt f 
Has Karl Marie kissed? 
"Did Karl kiss Mary?" 
for which we adopt the argument composition anal- 
ysis presented in Hinrichs and Nakazawa (1989): the 
subeat list of the auxiliary verb is partially instan- 
tiated in the lexicon and only becomes fully instan- 
tiated upon its combination with its verbal comple- 
ment, the main verb. The phrase structure rule that 
describes this construction is 1 
cat 0\]\] subcat 
cont 
I cat v fin + aux + subcat ( \['3"1l r¥1 ) Lcont \[\] I cat v lJ L, ub¢~t \[EI \[\] 
Though a head-driven generator must generate first 
the head of the rule, nothing prescribes the order of 
generation of the complements of the head. If the 
generator generates second the main verb then the 
subcat list of the main verb instantiates the subcat 
list of the head, and generation becomes a deter- 
ministic procedure in which complements are gener- 
ated in sequence. However, if the generator gener- 
ates second some complement other than the main 
verb, then the subcat list of the head contains no 
restricting information to guide deterministic gener- 
ation, and generation becomes a generate-and-test 
procedure in which complements are generated at 
random, only to be eliminated by further unifica- 
tions. Clearly then, the order of evaluation of the 
complements in a rule can profoundly influence the 
efficiency of generation, and an efficient head-driven 
generator must order the evaluation of the comple- 
ments in a rule accordingly. 
2.3 Off-line versus On-line 
Dynamic, on-line reordering can solve the ordering 
problem discussed in the previous subsection, but is 
rather unattractive: interpreting grammar rules at 
1For expository reasons, we refrain from a division 
between the subject and the other complements of a 
verb as in chapter 9 of Pollard and Sag (1994). The 
test-grammar does make this division and always guar- 
antees the correct order of the complements on the comps 
list with respect to the obliqueness hierarchy. Further- 
more, we use abbreviations of paths, such as coat for 
syasemlloc\[coat , and assume that the semantics princi- 
ple is encoded in the phrase structure rule. 
run time creates much overhead, and locally deter- 
mining the optimal evaluation order is often impos- 
sible. Goal-freezing can also overcome the ordering 
problem, but is equally unappealing: goal-freezing 
is computationally expensive, it demands the proce- 
dural annotation of an otherwise declarative gram- 
mar specification, and it presupposes that a gram- 
mar writer possesses substantial computational pro- 
cessing expertise. We chose instead to deal with the 
ordering problem by using off-line compilation to au- 
tomatically optimize a grammar such that it can be 
used for generation, without additional provision for 
dealing with the evaluation order, by our Earley gen- 
erator. 
3 Off-line Grammar Optimization 
Our off-line grammar optimization is based on a gen- 
eralization of the dataflow analysis employed in the 
DIA to a dataflow analysis for typed feature struc- 
ture grammars. This dataflow analysis takes as in- 
put a specification of the paths of the start category 
that are considered fully instantiated. In case of 
generation, this means that the user annotates the 
path specifying the logical form, i.e., the path cont 
(or some of its subpaths), as bound. We use the 
type hierarchy and an extension of the unification 
and generalization operations such that path anno- 
tations are preserved, to determine the flow of (se- 
mantic) information between the rules and the lexical 
entries in a grammar. Structure sharing determines 
the dataflow within the rules of the grammar. 
The dataflow analysis is used to determine the rel- 
ative efficiency of a particular evaluation order of 
the right-hand side categories in a phrase structure 
rule by computing the maximal degree of nondeter- 
minacy introduced by the evaluation of each of these 
categories. The maximal degree of nondeterminacy 
introduced by a right-hand side category equals the 
maximal number of rules and/or lexical entries with 
which this category unifies given its binding anno- 
tations. The optimal evaluation order of the right- 
hand side categories is found by comparing the max- 
imal degree of nondeterminacy introduced by the 
evaluation of the individual categories with the de- 
gree of nondeterminacy the grammar is allowed to 
introduce: if the degree of nondeterminacy intro- 
duced by the evaluation of one of the right-hand side 
categories in a rule exceeds the admissible degree 
of nondeterminacy the ordering at hand is rejected. 
The degree of nondeterminacy the grammar is al- 
lowed to introduce is originally set to one and con- 
secutively incremented until the optimal evaluation 
order for all rules in the grammar is found. 
3.1 Example 
The compilation process is illustrated on the basis 
of the phrase structure rule for argument composi- 
tion discussed in 2.2. Space limitations force us to 
175 
abstract over the recursive optimization of the rules 
defining the right-hand side categories through con- 
sidering only the defining lexical entries. 
Unifying the user annotated start category with 
the left-hand side of this phrase structure rule leads 
to the annotation of the path specifying the logical 
form of the construction as bound (see below). As a 
result of the structure-sharing between the left-hand 
side of the rule and the auxiliary verb category, the 
cont-value of the auxiliary verb can be treated as 
bound, as well. In addition, the paths with a value 
of a maximal specific type for which there are no 
appropriate features specified, for example, the path 
cat, can be considered bound: 
subcatbo..a 
cont b o ~. a 
~llb°~nd + \[ flnbound -- 8.UXbound 
+ , 53 , \[2\] , \[\]l.UXbo.nd ~ 
~ub~t (~I El', L, ub¢~t \[\]3157 
LcOntbo~.a \[\] 
On the basis of this annotated rule, we investigate 
the lexical entries defining its right-hand side cate- 
gories. The auxiliary verb category is unified with 
its defining lexical entries (under preservation of the 
binding annotations). The following is an example 
of such a lexical entry. (Note that subpaths of a path 
marked as bound are considered bound too.) 
c~ttbound V 
finbou.4 + 
~.UXbo,.~nd -I- 
subcat <\[contbou.4 ~> 
contbo..a I nucleusbo~.a I argbo..a 
The binding annotations of the lexical entries defin- 
ing the auxiliary verb are used to determine with 
how many lexical entries the right-hand side cate- 
gory of the rule maximally unifies, i.e., its maximal 
degree of nondeterminacy. In this case, the maxi- 
mal degree of nondeterminacy that the evaluation 
of the auxiliary verb introduces is very low as the 
logical form of the auxiliary verb is considered fully 
instantiated. Now we mark the paths of the defining 
lexical entries whose instantiation can be deduced 
from the type hierarchy. To mimic the evaluation 
of the auxiliary verb, we determine the information 
common to all defining lexical entries by taking their 
generalization, i.e., the most specific feature struc- 
ture subsuming all, and unify the result with the 
original right-hand side category in the phrase struc- 
ture rule. Because both the generalization and the 
unification operations preserve binding annotations, 
this leads (via structure-sharing) to the annotation 
that the logical form of the verbal complement can 
be considered instantiated. Note that the nonver- 
bal complements do not become further instantiated. 
By subsequent investigation of the maximal degree 
of nondeterminacy introduced by the evaluation of 
the complements in various permutations, we find 
that the logical form of a sentence only restricts the 
evaluation of the nonverbal complements after the 
evaluation of the verbal complement. This can be 
verified on the basis of a sample lexical entry for a 
main verb. 
"phon 
cat 
fin 
aux 
subcat 
lieben 
v 
< \[coat \['6\]\] !\[cont rT\]\] 
, r,o o, c°nt ' numeus \[loved r-#\] j 
The relative efficiency of this evaluation leads our 
compiler to choose 
\[ cat v fin 4- ~UX ~L 
Lcont \[\] 
cat {}\[~\] 
subcat -----, 
cont 
, \[\] aUX 
L,ub¢~t 531 \[\] 
\[i\],\[\] 
as the optimal evaluation order of our phrase struc- 
ture rule for argument composition. 
3.2 Processing Head 
The optimal evaluation order for a phrase structure 
rule need not necessarily be head-first. Our dataflow 
anMysis treats heads and complements alike, and in- 
cludes the head in the calculation of the optimal 
evaluation order of a rule. If the evaluation of the 
head of a rule introduces much nondeterminacy or 
provides insufficient restricting information for the 
evaluation of its complements, our dataflow analysis 
might not select the head as the first category to be 
evaluated, and choose instead 
subcat -----+ 
cont 
pat v >\] It at v fin 4- 
\[\] aux ~ux + , N, \[\] 
Lsubeat Fill \[\] L ~°nt \[\] ' 
as the optimal evaluation order. This clearly demon- 
strates an extremely important consequence of us- 
ing our dataflow analysis to compile a declarative 
grammar into a grammar optimized for generation. 
Empty or displaced heads pose us no problem, since 
the optimal evaluation order of the right-hand side 
of a rule is determined regardless of the head. Our 
dataflow analysis ignores the grammatical head, but 
identifies instead the 'processing head', and (no less 
176 
importantly) the 'first processing complement', the 
'second processing complement', and so on. 
4 Constraints on Grammar 
Our Earley generator and the described compiler 
for off-line grammar optimization have been exten- 
sively tested with a large HPSG grammar. This test- 
grammar is based on the implementation of an anal- 
ysis of partial vP topicalization in German (Hinrichs 
et al., 1994) in the Troll system (Gerdemann and 
King, 1994). Testing the developed techniques un- 
covered important constraints on the form of the 
phrase structure rules in a grammar imposed by the 
compiler. 
4.1 Complement Displacement 
The compiler is not able to find an evaluation or- 
der such that the Earley generator has sufficient re- 
stricting information to generate all subparts of the 
construction efficiently in particular cases of comple- 
ment displacement. More specifically, this problem 
arises when a complement receives essential restrict- 
ing information from the head of the construction 
from which it has been extracted, while, at the same 
time, it provides essential restricting information for 
the complements that stayed behind. Such a case is 
represented schematically in figure 1 (see next page). 
The first processing complement (el) of the head 
(H) has been displaced. This is problematic in case 
cl provides essential bindings for the successful eval- 
uation of the complement c2. cl can not be evalu- 
ated prior to the head and once H is evaluated it 
is no longer possible to evaluate cl prior to c2. 
An example of problematic complement displace- 
ment taken from our test-grammar is given in fig- 
ure 2 (see next page). The topicalized partial vP 
"Anna lichen" receives its restricting semantic infor- 
mation from the auxiliary verb and upon its eval- 
uation provides essential bindings not only for the 
direct object, but also for the subject that stayed 
behind in the Mittelfeld together with the auxiliary 
verb. These mutual dependencies between the sub- 
constituents of two different local trees lead either 
to the unrestricted generation of the partial vP, or 
to the unrestricted generation of the subject in the 
Mittelfeld. We handled this problem by partial exe- 
cution (Pereira and Shieber, 1987) of the filler-head 
rule. This allows the evaluation of the filler right 
after the evaluation of the auxiliary verb, but prior 
to the subject. A head-driven generator has to rely 
on a similar solution, as it will not be able to find a 
successful ordering for the local trees either, simply 
because it does not exist. 
4.2 Generalization 
A potential problem for our approach constitutes 
the requirement that the phrase structure rules in 
the grammar need to have a particular degree of 
specificity for the generalization operation to be 
used successfully to mimic its evaluation. This is 
best illustrated on the basis of the following, more 
'schematic', phrase structure rule: 
\[cat (}l~.\]\] \[i at v fin ~- >1 (~ ,ff\]NN subcat _.... 
ubcat ,~\],\[~ ' ' Lcont 
\[cont 
Underspecification of the head of the rule allows it to 
unify with both finite auxiliaries and finite ditransi- 
tive main verbs. In combination with the underspec- 
ification of the complements, this allows the rule not 
only to be used for argument composition construc- 
tions, as discussed above, but also for constructions 
in which a finite main verb becomes saturated. This 
means that the logical form of the nonverbal com- 
plements (if\] and \[~) becomes available either upon 
the evaluation of the complement tagged \[\] (in case 
of argument composition), or upon the evaluation 
of the finite verb (in case the head of the rule is 
a ditransitive main verb). As a result, the use of 
generalization does not suffice to mimic the evalua- 
tion of the respective right-hand side categories. Be- 
cause both verbal categories have defining lexical en- 
tries which do not instantiate the logical form of the 
nonverbal arguments, the dataflow analysis leads to 
the conclusion that the logical form of the nonver- 
bal complements never becomes instantiated. This 
causes the rejection of all possible evaluation orders 
for this rule, as the evaluation of an unrestricted non- 
verbal complement clearly exceeds the allowed max- 
imal degree of nondeterminacy of the grammar. We 
are therefore forced to split this schematic phrase 
structure rule into two more specific rules at least 
during the optimization process. It is important to 
note that this is a consequence of a general limita- 
tion of dataflow analysis (see also Mellish, 1981). 
5 Concluding Remarks 
An innovative approach to HPSG processing is de- 
scribed that uses an off-line compiler to automat- 
ically prime a declarative grammar for generation 
or parsing, and inputs the primed grammar to an 
advanced Earley processor. Our off-line compiler 
extends the techniques developed in the context of 
the DIA in that it compiles typed feature struc- 
ture grammars, rather than simple logic grammars. 
The approach allows efficient bidirectional process- 
ing with similar generation and parsing times. It 
is shown that combining off-line techniques with an 
advanced Earley-style generator provides an elegant 
solution to the general problem that empty or dis- 
placed heads pose for conventional head-driven gen- 
eration. 
The developed off-line compilation techniques 
make crucial use of the fundamental properties of the 
HPSG formalism. The monostratal, uniform treat- 
ment of syntax, semantics and phonology supports 
177 
l H \] C2 
Figure 1: Complement displacement. 
c at v 
subcat () 
cont\[~'\[\[ nucleus I arg\[ nucleus lover ...karl'... \]\] loved anna' . 
\[\] 
F cat ( )\[~ll F~/subcat 
Lcont 
"cat v 
fin 
Fat n Fat n 
subcat \['g'\] lease ~m \[~\] \[case 
cont cont 
slash {} 
lover cont \[\] nucleus \[loved ~N-'I\] 
is:L, ~- 
slash 
cont 
fin + 
aux + 
subcat (\[~\]) 
sl,.,h {D} 
eont I~llnueleuslarg \[\] 
\[\] 
Anna lieben wird 
Anna love will 
"Karl will love Anna" 
Figure 2: Example of problematic complement displacement. 
Karl. 
Karl. 
178. 
dataflow analysis, which is used extensively to pro- 
vide the information upon which off-line compilation 
is based. Our compiler uses the type hierarchy to de- 
termine paths with a value of a minimal type with- 
out appropriate features as bound. However, the 
equivalent of this kind of minimal types in untyped 
feature structure grammars are constants which can 
be used in a similar fashion for off-line optimization. 
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