20 
1965 International Conference on 
Computational Linguistics 
ENDOCENTRIC CONSTRUCTIONS AND TIlE COCKE 
PARSING LOGIC 
Jane J. Robinson 
The RAND Corporation 
1700 Main Street 
Santa Monica D California 90406 
h.- Uo/~ x 
I _~, ..~.' ~ '%. "~,.\ 
Robinson 2 
ABSTRACT 
Automatic syntactic analysis is simplified by dis- 
engaging the grammatical rules, by means of a parsing 
logic, from the computer routines that apply them. A case 
in point is the John Cocke logic. It iterates on five 
simple parameters and finds all structures permitted by 
the grammar, thus testing the rules, which can then be 
changed without changing the routines. The rules them- 
selves need not be ordered so far as the logic of the 
system is concerned. However, in operating with an IC 
grammar, rules for bracketing endocentric constructions 
must be made quite complex merely to avoid multiple analy- 
ses of unambiguous or trivially ambiguous expressions. 
The rules can be simplified if they are classified and 
if the system is provided with an additional capability 
for applying them in a specified order. Although an 
additional parameter is introduced into the system, the 
disengagement of grammar from routine is preserved. The 
additional parameter controls the direction, left-to-right 
or right-to-left, in which constructions are put together. 
The decision as to which direction should be specified is 
a grammatical decision, and is related to Yngve's hypothe- 
sis of asymmetry in language. It does not affect the opera- 
tion of the parsing logic. 
Robinson 3 
ACKNOWLEDGMENTS 
I wish to acknowledge the assistance of M. Kay and 
S. Marks in discussing points raised in the paper and in 
preparing the flowchart. A more general acknowledgment is 
due to D. G. Hays, who first called my attention to the 
problem of orderin~ the attachment of elements. 
Robinson 4 
ENDOCENTRIC CONSTRUCTIONS AND THE 
COCKE PARSING LOGIC 
Automatic sentence structure determination (SSD) is 
greatly simplified if, through the intervention of a 
parsing logic, the grammatical rules that determine the 
structure are partially disengaged from the computer rou- 
tines that apply to them. Some earlier parsing programs 
analyzed sentences by routines that branched according to 
the grammatical properties or signals encountered at par- 
ticular points in the sentence, making the routines them- 
selves serve as the rules. This not only required separate 
programs for each language, but led to extreme proliferation 
in the routines, requiring extensive rewriting and debu~gin~ 
with every discovery and incorporation of a new ~rammatical 
feature. More recently, programs for SSD have employed 
generalized parsing logics, applicable to different lan- 
guages and providing primarily for an exhaustive and sys- 
tematic application of a set of rules. (1,2,5,5) The rules 
themselves can be changed without changing the routines 
that apply them, and the routines consequently take fuller 
advantage of the speed with which digital computers can 
repeat the same sequence of instructions over and over 
again, changing only the values of some parameters at each 
cycle. 
Robinson S 
The case in point is the parsing logic (PL) devised 
by John Cocke in 1960, for applying the rules of a context- 
free phrase structure grammar (PSG), requiring that each 
structure recognized by the grammar be analyzed into two 
and only two immediate constituents.(I) 
Although all PSGs appear to be inadequate in some 
important respects to the task of handling natural lan- 
guage, they still form the base of the more powerful 
transformational grammars, which are not yet automated 
for SSD. Moreover, even their severest critic acknowledges 
that "The PSG conception of grammar...is a quite reasonable 
theory of natural language which unquestionably formalizes 
many actual properties of human language."(6,P "78) Both 
theoretically and empirically the development and automatic 
application of PSGs are of interest to linguists. 
The PSG on which the Cocke Pl, operates is essentially 
a table of constructions. Its rules have three entries, 
one for the code (a descriptor) of the construction, the 
other two specifying the codes of the ordered pair of 
immediate constituents out of which it may be formed. 
The logic iterates in five nested loops, controlled by 
three simple parameters and two codes supplied by the 
grammar. They are: i) the string length, starting with 
length 2, of the segment being tested for constructional 
Robinson 6 
status; 2) the position of the first word in the tested 
string; 3) the length of the first constituent; 4) the 
codes of the first constituent; and 5) the codes of the 
second constituent. 
After a dictionary lookup routine has assi~.ned grammar 
codes to all the occurrences in the sentence or total 
string to be parsed (it need not be a sentence), the PL 
operates to offer the codes of pairs of adjacent segments 
to a parsing routine that tests their connectability by 
looking them up in the stored table of constructions, i.e., 
in the grammar. If the ordered pair is matched by a pair 
of ICs in the table, tile code of the construction formed 
by the ICs is added to the list of codes to be offered 
for testin~ when iterations are performed on longer strings. 
In the RAND program for parsing English, the routines 
produce a labeled binary-branching tree for every complete 
structural analysis. There will be one tree if the grammar 
recognizes the string as well-formed and syntactically 
unambiguous; more than one if it is recognized as ambiguous. 
Even if no complete analysis is made of the whole string, 
a resum~ lists all constructions found in the process, 
including those which failed of inclusion in larger con- 
structions. (8,9) 
*This interaction between a PL and a routine for testing 
the connectability of two items is described in somewhat 
greater detail in Hays (2). 
Rob ins on 7 
Besides simplifying the problem of revising the grammar 
by separating it from the problem of application to sen- 
tences, the PL, because it leads to an exhaustive application 
of the rules, permits a rigorous evaluation of the 
grammar's ability to assign structures to sentences and 
also reveals many unsuspected yet legitimate ambiguities 
in those sentences.(4, 7) But because of the difficulties in- 
herent in specifying a sufficiently discriminatory set of 
rules for sentences of any natural language and because 
of the very many syntactic ambiguities, resolvable only 
through lar~er context, this method of parsing produces 
a long list of intermediate constructions for sentences 
of even modest length, and this in turn raises a storage 
prob lem. 
By way of illustration, consider a string of four 
occurrences, x I x 2 x 3 x4, a dictionary that assigns a 
single grammar code to each, and a grammar that assigns 
a unique construction code to every different combination 
of adjacent segments. Given such a grammar, as in Table I, 
the steps in its application to the string by the parsing 
routines operating with the Cocke PL are represented in 
Table II. (The preliminary dictionary lookup assigning 
the original codes to the occurrences is treated as equiv- 
alent to iterating with the parameter for string length 
set to I). 
Robinson 8 
Table I 
Rule # ICl IC2 CO 
I. A B E 
2o B C F 
3. c D o 
4. A F H 
5. E C I 
6. B G J 
7. F D I< 
ICl: 
IC2: 
code of first constituent 
code of second constituent 
Rule # iCl 102 CO 
8. A J L 
9. A K M 
lO. E G N 
ii. H D 
12. I D P 
13. A C Q 
14. etc. 
CC: code of construction 
Table II 
Steps 
¢i ~ M W P C(P) C(Q) C(M) Rule ~ Combined Structure Assigned 
I. i I i A A 
2. 1 2 i B B 
3. I 3 \] c c 
4. 1 4 1 D D 
Dictionary x I 
lookup x 2 
assio~ning x 3 
codes to: x 4 
5. ? 
6. 2 
7. 2 
8. 3 
9. 3 
I0. x 
ll. 3 
12. 4 
13. 4 
14. 4 
15. 4 
16. 4 
#: 
P: 
c(P). 
i 1 
2 i 
3 1 
1 1 
! 2 
2 I 
2 
1 1 A 
I I ,'. 
I o E 
i 3 H 
1 3 i 
A R 
B C F 
C D G 
A F H 
~ C I 
B G J 
F D K 
J L 
i,; M 
O >T 
D i' 
stel; number 
strinj \].en~Tth of segment 
It 
3. 
o 
5. 
6. 
7. 
~o 
9. 
\].0. 
Ii. 
12. 
lenr'th of first construction 
s t,-ing 
code of first construction 
1+2 (Xl+X 2 ) 
2+3 (x2~x 3) 
~+4 (x3+x 4) 
5+3 < (Xl+~2)~," 3 ) 
• 2+7 (x2(x3+x 4) ) 
/ X 6~ (~x2+. 3)x4) 
c(M). 
i+i0 
!+ll 
5+7 
8+4 
9+4 
(x1(x2(x3+x4))) 
(Xl((x2+x3)%)) 
( (:c I ,x~) (~ 3÷~4) ) 
( (xj (x2+x 5) )xg) 
(((x l+x2)x ~)xL~) 
code of second const, string 
code for string, to be stored 
when C(P) and C(Q) are matched 
in the o~r_ammar. 
C(M) = CC of crammar. 
The boxed section represents the PL iterations. 
Robinson 9 
With such a grammar, the number of constructions to 
be stored and processed through each cycle increases in 
proportion to the cube of the number of words in the 
sentence. If the dictionary and grammar assign more than 
one code to occurrences and constructions, the number may 
grow multiplicatively, making the storage problem still 
more acute. For example, if x I were assigned two codes 
instead of one, additional steps would be required for 
every string in which x I was an element and iteration on 
string length 4 would require twice as many cycles and 
twice as much storage. 
Of course, reasonable grammars do not provide for 
combining every possible pair of adjacent segments into 
a construction, and in actual practice the growth of the 
construction list is reduced by failure to find the two 
codes presented by the PL, when the grammar is consulted. 
If Rule i is omitted from the grammar in Table I, then 
steps S, 9, 14, and 16 will disappear from Table II and 
both storage requirements and processing time will be cut 
down. Increasing the discriminatory power of the grammar 
through refining the codes so that the first occurrence 
must belong to class Aa and the second to class Bb in 
order to form a construction provides this limiting effect 
in essentially the same way. 
Robinson I0 
Another way o£ limiting the growth o£ the stored 
constructions is to take advantage of the fact that in 
actual grammars two or more different pairs of constituents 
sometimes combine to produce the "same" construction. 
Assume that A and F (Table I) combine to form a construc- 
tion whose syntactic properties are the same, at least 
within the discriminatory powers of the grammar, as those 
of the construction formed by E and C. Then Rules 4 and S 
can assign the same code, }l, to their constructions. In 
consequence, at both steps 8 and 9 in the parsing (Table 
If), |1 will be stored as the construction code C(M) for 
the string x I x 2 x3, even though two substructures are 
recorded for it: i.e. (Xl(X 2 + x3) ) and ((x I + x2)x3). 
The string can be marked as having more than one structure, 
but in subsequent iterations on string length 4, only one 
concatenation of the string with x 4 need be made and step 
16 can be omitted. When the parsing has terminated, all 
substructures of completed analyses are recoverable, 
including those of marked strings. 
Eliminating duplicate codes for the same string from 
the cycles of the PL results in dramatic savings in time 
and storage, partly because the elimination of any step 
has a cumulative effect, as demonstrated previously. In 
addition, opportunities to eliminate duplicates arise 
frequently, in English at least, because of the frequent 
Rob in s on 11 
occurrence o£ endocentric constructions, .constructions 
whose syntactic properties are largely the same as those 
o£ one of their elements--the head. In English~ noun 
phrases are typically endocentric, and when a noun head 
is flanked by attributives as in a phrase consisting of 
article, noun, prepositional phrase (A N PP), the require- 
ment that constructions have only two ICs promotes the 
assignment of two structures, (A(N+PP)) and (~A+N) PP), 
unless the grammar has been carefully formulated to avoid 
it. Since NPs of this type are ubiquitous, occurrinp, 
as subjects, objects of verbs, and objects of prepositions, 
duplicate codes for them are likely to occur at several 
points in a sentence. 
Consideration of endocentric constructions, however, 
raises other questions, some theoretical and some practi- 
cal, suggesting modification of the grammar and the 
parsing routines in order to represent the language more 
accurately or in order to save storage, or both. Theoreti- 
cally, the problem is the overstructuring of noun phrases 
by the insistence on two ICs and the doubtful propriety 
of permitting more than one way of structuring them. 
Practically, the problem is the elimination of duplicate 
construction codes stored for endocentric phrases when 
the codes are repeated for different string lengths. 
Robinson 12 
Consider the noun phrase subject in All the old men 
on the corner sta.red. Its syntactic properties are 
essentially the same as that of men. But fifteen other 
phrases, all made up from the same elements but varying 
in length, also have the same properties. They are 
shown below: 
Table III 
Length 
I. 7 
2. 6 
5. 6 
4. 6 
5. 5 
6. 5 
7. 5. 
8. 4 
9. 4 
i0. 3 
ii. 3 
12. 3 
13. 2 
14. 2 
15. 2 
16. 1 
Noun phrase 
All the old men on the corner 
The old men on the corner 
All the men on the corner 
All old men on the corner 
Old men on the corner 
The men on the corner 
All men on the corner 
Men on the corner 
All the old men 
The old men 
All the men 
All old men 
Old men 
The men 
All men 
Men 
(stared) 
A reasonably good grammar should provide for the 
recognition of all sixteen phrases. This is not to say 
that sixteen separate rules are required, although this 
would be one way of doing it. Minimally, the grammar must 
provide two rules for an endocentric NP, one to combine 
the head noun or the string containing it with a preceding 
attributive and another to combine it with a following 
Robinson 13 
attributive. The codes for all the resulting constructions 
may be the same, but even so, the longest phrase will re- 
ceive four different structural assignments or bracketings 
as its adjacent elements are gathered together in pairs; 
(all (the (old (men (on the corner))))) 
(all (the ((old men) (on the corner)))) 
(all ((the (old men)) (on the corner))) 
and ((all (the (old men))) (on the corner)) 
If it is assumed that the same code, say that of a 
plural NP, has been assigned at each string length, it is 
true that only one additional step is needed to concatenate 
the string with the following verb when the PL iteration 
is performed for string length 8. But meanwhile a number 
of intermediate codes have been stored during iterations 
on string lengths 5, 6, and 7 as the position of the first 
word of the tested string was advanced, so that the list 
also contains codes for: 
men on the corner stared (length 5) 
old men on the corner stared (length 6) 
and the old men on the corner stared (length 7) 
Again, the codes may be the same, but duplicate codes will 
not be eliminated from processing if they are associated 
with different strings, and strings of different length are 
treated as wholly different by the PL, regardless of over- 
lap. If this kind of duplication is to be reduced or 
name ly: 
Robinson 14 
avoided, a different procedure is required from that avail- 
able for the case of simple duplication over the same 
string. 
But first a theoretical question must be decided. 
Is the noun phrase, as exemplified above, perhaps really 
four-ways ambiguous and do the four different bracketings 
correlate systematically with four distinct interpretations 
or assignments of semantic structure? (Cf" 4,7) And if so, 
is it desirable to eliminate them? It is possible to argue 
that some of the different bracketings do correspond to 
different meanings or emphases, or--in earlier transforma- 
tional terms--to different orderings in the embeddings of 
the men were old and the men were on the corner into all the 
men stared. Admittedly the native speaker can indicate 
contrasts in meaning by his intonation, emphasizing in one 
reading that all the men stared and in another that it was 
all the ol___dd men who stared; and the writer can resort to 
italics. But it seems reasonable to assume that there is 
a normal intonation for the unmarked and unemphatic phrase 
and that its interpretation is structurally unambiguous. 
In the absence of italics and other indications, it seems 
~_~_reasonable to produce four different bracketings at every 
encounter with an NP of the kind exemplified. 
Robinson 15 
One way to reduce the duplication is to write the 
grammar codes so that, with the addition of each possible 
element, the noun head is assigned a different construction 
code whose distribution as a constituent in larger construc- 
tions is carefully limited. For the sake of simplicity, 
assume that the elements of NPs have codes that reflect, 
in part, their ordering within the phrase and that the NP 
codes themselves reflect the properties of the noun head 
in first position and are subsequently differentiated by 
codes in later positions that correspond to those of the 
attributes. Let the codes for the elements be 1 (all), 
2 (the), 3 (old), 4 (men), 5 (on the corner). Rules may 
be written to restrict the combinations, as follows: 
Robinson 16 
Tab le IV 
R# ICI IC2 CC 
i, 1+4 ÷41 
2. 2+4 ÷42 
3. 3+4 ÷43 
4. 4+5 ÷45 
5. i + 42 ÷ 412 
6. 1 + 43 ÷ 413 
7. 2 + 43 ÷ 423 
8. I + 423 ÷ 4123 
9. 1 + 45 ÷ 41S 
10. 2 ÷ 45 ÷ 42S 
II. 3 + 45 ÷ 435 
12. 2 + 435 ÷ 4235 
13. 1 ÷ 4235 ÷ 41235 
(all men) 
(the men) 
(old men) 
(men on the corner) 
(all the men) 
(all old men) 
(the old men) 
(all the old men) 
(all men on the corner); but not 
"41 + S ÷ 415 
(the men on the corner); but not 
*42 + 5 ÷ 425 
(old men on the corner); but not 
*43 + 5 ÷ 435 
(the old men on the corner); but not 
*423 + 5 ÷ 4235 
(all the old men on the corner); but 
not "4123 + 5 ÷ 41235 
With these rules, the Rrammar provides for only one 
structural assignment to the string: (all (the (old (men + 
on the corner)))). 
This method has the advantage of acknowledging the 
general endocentricity of the NP while allowing for its 
limitations, so that where the subtler differences among 
NPs are not relevant, they can be ignored by ignoring 
certain positions of the codes, and where they are relevant, 
the full codes are available. The method should lend 
Robinson 17 
itself quite well to code matching routines for connect- 
ability. However, if carried out fully and consistently, 
it greatly increases the length and complexity of both 
the codes and the rules, and this may also be a source of 
problems in storage and processing time. (cf. Flays, 2) 
Another method is to make use of a classification of 
the rules themselves. Since the lowest loop of the PL 
(see Fig. I) iterates on the codes of the second constitu- 
ents, the rules against which the paired strings are 
tested are stored as ordered by first IC codes and sub- 
ordered by second IC codes. If the iterations of the 
logic were differently ordered, the rules would also be 
differently ordered, for efficiency in testing. In other 
words, the code of one constituent in the test locates 
a block of rules within which matches for all the codes 
of the other constituent are to be sought; but the hierarchy 
of ordering by one constituent or the other is a matter 
of choice so long as it is the same for the PL and for storing 
the table of rules that constitute the grammar. In writing 
and revising the rules, however~ it proves humanly easier 
if they are grouped according to construction types. 
Accordingly, all endocentric NPs in the RAND grammar are 
given rule identification tags with an A in first position. 
Within this grouping, it is natural to subclass the rules 
according to whether they attach attributives on the right 
Robinson 18 
or on the left of the noun head. If properly formalized, 
this practice can lead to a reduction in the multiple 
analyses of NPs with fewer rules and simpler codes than 
those of the previous method. 
As applied to the example, the thirteen rules and 
five-place codes of Table IV can be reduced to two rules 
with one-place codes and an additional feature in the rule 
identification tag. 
*AI 
The rules can be written as: 
1 N N 
2 
3 
$A2 N 4 N 
Although the construction codes are less finely differen- 
tiated, the analysis of the example will still be unique, 
and the number of abortive intermediate constructions will 
be reduced. To achieve this effect, the connectability 
test routine must include a comparison of the rule tag 
associated with each C(P) and the rule tags of the grammar. 
If a rule of type *A is associated with the C(P), that is, 
if an *A rule assigned the construction code to the string 
P which is now being tested as a possible first constitu- 
ent, then no rule of type $A can be used in the current 
test. For all such rules, there will be an automatic 
"no match" without checking the second constituent codes. 
(See Fig. I.) As a consequence of this restriction, in 
Robinson 19 
the final analysis, the noun head will have been com- 
bined with all attributives on the right before acquiring 
any on the left. 
To be sure, the resume of intermediate constructions 
will contain codes for ol___dd men, the old men, and all the 
ol__.dd me__n_n , produced in the course of iterations on string 
lengths 2, 3, and 4, but only one structure is finally 
assigned to the whole phrase and the intermediate dupli- 
cations of codes for strings of increasing length will 
be fewer because of the hiatus at string length 5. Of 
course, in the larger constructions in which the NP par- 
ticipates, the reduction in the number of stored inter- 
mediate constructions will be even greater. 
Provisions may be made in the rules for attaching 
still other attributives to the head of the NP without 
great increase in complexity of rules or multiplication 
of structural analyses. Rule $A2, for example, could 
include provision for attaching a relative clause as well 
as a prepositional phrase, and while a phrase like the 
men on the corner who were sad might receive two analyses 
unless the codes were sufficiently differentiated to pre- 
vent the clause from being attached to corner as well as 
to me___n, at least the further differentiation of the codes 
need not also be multiplied in order to prevent the multiple 
analyses arising from endocentricity. 
Robinson 20 
Similarly, for verb phrases where the rule must allow 
for an indefinite number of adverbial modifiers, a single 
analysis can be obtained by marking the strings and the 
rules and forcing a combination in a single direction. In 
short, although the Cocke PL tends to promote multiple analy- 
sis of unambiguous or trivially ambiguous endocentric 
phrases, at the same time increasing the problem of storing 
intermediate constructions, the number of analyses can be 
greatly reduced and the storage problem greatly alleviated 
if the rules of the grammar recognize endocentricity wherever 
possible and if they are classified so that rules for endo- 
centric constructions are marked as left (*) or right ($), 
and their order of application is specified. 
A final theoretical-practical consideration can at 
least be touched on, although it is not possible to develop 
it adequately here. The foregoing description provided for 
combining a head with its attributives (or dependents) on the 
right before combining it with those on the left, but 
either course is possible. Which is preferable depends 
on the type of construction and on the language generally. 
If Yngve's hypothesis that languages are essentially 
asymmetrical, tending toward right-branching constructions 
to avoid overloading the memory, is correct, then the 
Robinson 21 
requirement to combine first on the right is preferable. (10) 
This is a purely grammatical consideration, however, and 
does not affect the procedure sketched above, in principle. 
For example, consider an endocentric construction of string 
length 6 with the head at position 3, so that its extension 
is predominantly to the right, thus: 1 2 (3) 4 5 6. If all 
combinations were allowed by the rules, there would be 
thirty-four analyses. If combination is restricted to 
either direction, left or right, the number of analyses is 
reduced to eleven. However, if the Cocke PL is used to 
analyze a left-branching language, making it preferable to 
specify prior combination on the left, then the order of 
nesting of the fourth and fifth loops of the PL should be 
reversed (Fig. I) and the rules of the grammar should be 
stored in order of their second constituent codes, subordered 
on those of the first constituents. 
Robinson 22 
N" 
P: 
Q: 
M: 
Fig. I 
FLOWCHART FOR THE COCKE PL 
sentence length 
string length of first 
constituent 
string length of second 
constituent 
P+Q - string length of 
construction 
W" 
L(W) : 
C(P): 
c (Q) : 
number of first word of M 
N-M+I = limit of first word 
code of first constituent 
code of second constituent 
l~ M+I÷MI<~ > 
CONSTRUCTION CODE 
ASSOCIATED WITH M, 
AND KEEP TRACK 
INPUT SENTENCE OF LENGTH N 
do dictionary lookup 
associate grammar codes 
with words and keep track 
\[SET M EQUAL TO 2\[ 
> 
ISET L(W) EQUAL TO (N-M+I) 
l .... SET W EQUAL TO I 
,< 
~OMPARE W AND L(W)~ 
\[SET p EQUAL iO I l 
~OMPARE P AND_~M~---- "\] W+: 
OUTPUT 
l 
W+I÷W I 
no more t 
.... l P+I÷P 
mo re 
RESET TO FIRST C(Q), GET 
NEXT C (P) 
IM-P  I 
COMPARE C(P), C(Q) WITH DE~ IRST IC CODE, SECOND IC CO 
IN THE GRAMMAR 
match ~no match 
STORE RULE # AND (~EST FOR MORE C(Q) S~ k'- -j 
no more ~ ~ more 
Robinson 23 

REFERENCES 

}lays, D. G., "Automatic Language-Data Processing," 
Computer Applications in the Behavioral Sciences, 
Chapter 17, Prentice-Hall, 1962. 

}lays, D. G. "Connectability Calculations, syntactic 
Functions, and Russian Syntax," Mechanical Transla- 
tio.___~n, Vol. 8, No. 1 (August 1964). 

Kuno, S., and A. G. Oettinger, "Multiple-path Syntactic 
Analyzer," Mathematical Linguistics and Automatic 
Translation, Report No. NSF-8, Sec. TT-The Computa- 
tion Laboratory of }larvard University, 1965. 

Kuno, S., and A. G. Oettinger, "Syntactic Structure and 
Ambiguity of English," AFIPS Conference Proceedings 
Vol. 24, 1965 Fall Joint--~mputer Con±erence. 

National Physical Laboratory, 1961 International 
Conference o__n_n Machine Trans-T~ion of Languages and 
Applied Language Analysis, Vol. 2,-\[\[. M. Stationery 
Office, 1962. 

Postal, P. M. Constituent Structure, Publication Thirty 
of the Indiana Univers~rch Center in Anthro- 
pology, Folklore, and Linguistics, January 1964. 

Robinson, J.) "Automated Grammars as Linguistics Tools," 
(Unpublished), Presented at the Thirty=ninth Annual 
Meeting of the Linguistic Society of America, New 
York, December 1964. 

Robinson, J., The Automatic Recognition of Phrase 
Structure and Paraphrase, RM-4005-PR (Abridlged), 
The RAND Corporation, Santa Monica, December 1964. 

Robinson, J., Preliminary Codes and Rules for the Automatic 
Parsing of English, RM-S339-PR, =The RAN\]) Corporation, 
Santa Mort}ca, December 1962. 

Yngve, V. li., "A Model and an Hypothesis for Language 
Structure," Proceedings of the American Philosophical 
Society, Vol. 104, No. S--\[Oct-~e-r 1960). 
