cmp-lg/9405025 26 May 94 as has recognized the rst symbol b oth to the time complexityamounts and to much the nondeterminism which space complexity is detrimental b egin with the samegrammar few contains grammars symbols e g vantage algorithm very e cient parsing algorithm related to Tomita s e cient which cannot handle leftoften recursion used and as is an generallyat alternative the less to same top down time TD Since is parsing LC able parsing to is deal a with very left simple recursion parsing technique it and is where of lo okahead can handle the class of LC which In this pap er we relate a number of parsing algorithms puter science has b een used in di erent guises in various areas of com Left corner represent the same sub derivation rithms parsing search NWO under grant p ossible prop erty that theing table namely will how to contain obtain asquestion a which little parsing has entries algorithm come with up as of the others in the areap of ortunity to tabular improve pars some algorithms based on features underlying ideas We show that these Nondeterministic By relating existing ideas we hop e to provide an op next Supp orted by the Dutch Organisation for Scienti c Re AN have tabular theory however step is but A second purp ose of this pap er is to answer a and not LC b een OPTIMAL without predict Deterministic LC parsing with Earley s the and algorithms A parsing developed which Introduction many rules empty string LC algorithms are based on the same which Abstract all the University of Nijmegen Department of parsing is algorithm b ecomes 1 aforementioned is j p ossibility orooiveld Toerno include and in a 2 parsing whose X very j a noticeable of such an the After deterministic TABULAR parallel It di erent that right hand foundation of a strategy has k an grammars rules two Mark Jan one algorithm LC k when markjan cs kun nl areas symbols it will entries parser disad which algo sides This ED the of Nijmegen The Netherlands Nederhof PARSING tive in case we havethe e g left hand the sides rules of the rules are the same neous pro cessing where again then a In case the stackthe algorithm is grammar very can nondeterministic b e for handled almost deterministically of sub derivations that each state representsalization the computation This of can a bnumber e number of informally explained entries by increases the the the fact number of states may lead to an increasing as a tabular realisation ofpaths nondeterministic LR parsing allows sharing of computation b etween di erent search cussed parsing algorithms mentioned ab ove have not b een dis each tabular parsing which canand b e ELR describ parsing ed are as obvious follows solutions to a problem of lead purp ose symbols realisation tions b etween these algorithms then rithm represent b een describ ed ingorithm their from own the right existingof literature tabular but parsing they algorithms havemon and not pre xes a parallel parsinggorithms al capable of simultaneous pro cessing ELR of and all common pre x com CP therefore parsing go which one are step al further and discuss extended LR of its tabular realisation A rst attempt to solve this problem is to use predic certain At A To In LR second to PLR parsing will not improve the general parsing it this the For example Tomita s algorithm can b e seen which together e cient is PLR of o ccurring Computer Science b est an grammar p oint inevitable using this purp ose algorithm working overlapping p owerful also ELR and CP parsing are the foundation is not the empty string but now of parsing pap er we in tabular a of a common pre x the If the number of states o ccur parse on the use however of this ALGORITHM that author s is the algorithms working existing the parse table of the tabular re parsing to as PLR table collection at stack term make pap er entries A sophistication some parsing knowledge where literature on algorithms of state explicit is in p oint a of the to 1 stack the the provided that allows to sub derivations and e ciency show that original indicate some the is increased the parse parse on B The there which However provided simulta connec A a various states stack table main table algo is For CP We the in B 2 a
notation of rules A A with the same which may lead to work b eing rep eated during parsing
1 2
lhs is often simpli ed to A j j Furthermore the parse forest a compact representa
1 2
A rule of the form A is called an epsilon rule tion of all parse trees which is output by a tabular
algorithm may in this case not b e optimally dense
We assume grammars do not have epsilon rules unless
stated otherwise
We conclude that we have a tradeo b etween the case
The relation P is extended to a relation on V V
that the grammar allows almost deterministic parsing
as usual The re exive and transitive closure of is
and the case that the stack algorithm is very nondeter
denoted by
ministic for a certain grammar In the former case so
We de ne B A if and only if A B for some
phistication leads to less entries in the table and in the
The re exive and transitive closure of is denoted by
latter case sophistication leads to more entries pro
and is called the left corner relation
vided this sophistication is realised by an increase in
We say two rules A and B have a com
the number of states This is corrob orated by empirical
1 2
mon pre x if and for some
data from which deal with tabular LR parsing
1 1 2 2 1
and where
2
As we will explain CP and ELR parsing are more
A recognition algorithm can b e sp eci ed by means
deterministic than most other parsing algorithms for
of a push down automaton A T Alph Init Fin
many grammars but their tabular realizations can
which manipulates con gurations of the form v
never compute the same sub derivation twice This rep
where Alph is the stack constructed from left
resents an optimum in a range of p ossible parsing algo
to right and v T is the remaining input
rithms
The initial con guration is Init w where Init
This pap er is organized as follows First we discuss
Alph is a distinguished stack symbol and w is the input
nondeterministic left corner parsing and demonstrate
The steps of an automaton are sp eci ed by means of the
how common pre xes in a grammar may b e a source of
relation Thus v v denotes that v
bad p erformance for this technique
is obtainable from v by one step of the automaton
Then a multitude of parsing techniques which ex
The re exive and transitive closure of is denoted by
hibit b etter treatment of common pre xes is dis
The input w is accepted if Init w Fin
cussed These techniques including nondeterministic
where Fin Alph is a distinguished stack symbol
PLR ELR and CP parsing have their origins in theory
of deterministic parallel and tabular parsing Subse
LC parsing
quently the application to parallel and tabular parsing
is investigated more closely
For the de nition of left corner LC recognition we
need stack symbols items of the form A
Further we brie y describ e how rules with empty
where A is a rule and Remember that
right hand sides complicate the parsing pro cess
we do not allow epsilon rules The informal meaning
The ideas describ ed in this pap er can b e generalized
of an item is The part b efore the dot has just b een
to head driven parsing as argued in
recognized the rst symbol after the dot is to b e rec
We will take some lib erty in describing algorithms
ognized next For technical reasons we also need the
from the existing literature since using the original de
items S S and S S where S is a fresh
scriptions would blur the similarities of the algorithms
symbol Formally
to one another In particular we will not treat the use
of lo okahead and we will consider all algorithms work
LC y
I f A j A P A S g
ing on a stack to b e nondeterministic We will only
y
describ e recognition algorithms Each of the algorithms
where P represents the augmented set of rules consist
can however b e easily extended to yield parse trees as
ing of the rules in P plus the extra rule S S
a side e ect of recognition
Algorithm Left corner
LC LC
A T I Init Fin Init S S Fin
The notation used in the sequel is for the most part
S S Transitions are allowed according to the
standard and is summarised b elow
following clauses
A context free grammar G T N P S consists of
two nite disjoint sets N and T of nonterminals and
B C av
terminals resp ectively a start symbol S N and a
B C A a v
y
nite set of rules P Every rule has the form A
where there is A a P such that A C
where the left hand side lhs A is an element from N
A a av A a v
and the right hand side rhs is an element from V
B C A v
where V denotes N T P can also b e seen as a
B C D A v
relation on N V
y
where there is D A P such that D C
We use symbols A B C to range over N symbols
B A A v B A v
a b c to range over T symbols X Y Z to range over
V symbols to range over V and v w x in the The conditions using the left corner relation
to range over T We let denote the empty string The rst and third clauses together form a feature which is
called top down TD ltering TD ltering makes sure for some grammar G with LC parsing for some gram
that sub derivations that are b eing computed b ottom mar G which results after applying a transformation
up may eventually grow into sub derivations with the re called left factoring
quired ro ot TD ltering is not necessary for a correct Left factoring consists of replacing two or more rules
algorithm but it reduces nondeterminism and guar A j j with a common pre x by the rules
1 2
antees the correct pre x property which means that in A A and A j j where A is a fresh non
1 2
case of incorrect input the parser do es not read past the terminal The e ect on LC parsing is that a choice
rst incorrect character b etween rules is p ostp oned until after all symbols of
are completely recognized Investigation of the next k
Example Consider the grammar with the following
symbols of the remaining input may then allow a choice
rules
b etween the rules to b e made deterministically
The PLR algorithm is formalised in by trans
E E T j T E j T
forming a PLR k grammar into an LL k grammar
T T F j T F j F
and then assuming the standard realisation of LL k
F a
parsing When we consider nondeterministic top down
parsing instead of LL k parsing then we obtain the
It is easy to see that E E T E T T F T
new formulation of nondeterministic PLR parsing
contains The relation but from the re exive closure
b elow
F and from the transitive closure it also contains F
We rst need to de ne another kind of item viz of
it also contains F E
the form A such that there is at least one rule of
The recognition of a a is realised by
the form A for some Formally
E E a a
PLR y
I f A j A P A S g
E E F a a
E E T F a
PLR
Informally an item A I represents one or
E E T T F a
LC
more items A I
E E T T F a
Algorithm Predictive LR E E T T F F a
PLR PLR
A T I Init Fin Init S Fin E E T T F
S S and de ned by
E E E T
E E
B av B A a v
y
where there are A a B C P such that
Note that since the automaton do es not use any lo oka
A C
head Step may also have replaced T F by
any other item b esides T T F whose rhs starts
A av A a v
y
with T and whose lhs satis es the condition of top
where there is A a P
down ltering with regard to E i e by T T F
B A v B D A v
y
E T E or E T 2
where A P and where there are D
y
C A B C P such that D
LC parsing with k symbols of lo okahead can handle
B A v B A v
deterministically the so called LC k grammars This
1 y
class of grammars is formalized in How LC pars where A P and where there is B A
y
P
ing can b e improved to handle common su xes e
ciently is discussed in in this pap er we restrict our
Example Consider the grammar from Example
attention to common pre xes
Using Predictive LR recognition of a a is realised by
E a a
PLR ELR and CP parsing
E F a a
In this section we investigate a number of algorithms
E T F a
which exhibit a b etter treatment of common pre xes
E T T a
E T T a
Predictive LR parsing
Predictive LR PLR parsing with k symbols of lo oka
E E
head was introduced in as an algorithm which yields
e cient parsers for a subset of the LR k grammars
Comparing these con gurations with those reached by
and a sup erset of the LC k grammars How determin
the LC recognizer we see that here after Step the
istic PLR parsing succeeds in handling a larger class
stack element T T represents b oth T T F
of grammars the PLR k grammars than the LC k
and T T F so that nondeterminism is reduced
grammars can b e explained by identifying PLR parsing
Still some nondeterminism remains since Step could
1
also have replaced T F by E T which repre
In a di erent de nition of the LC k grammars may
sents b oth E T E and E T 2 b e found which is not completely equivalent
LC
Extended LR parsing in I and one for nonkernel items the others These
are de ned by
An extended context free grammar has right hand sides
consisting of arbitrary regular expressions over V This
goto Q X
1
requires an LR parser for an extended grammar an
closure f A X j A X Q
ELR parser to b ehave di erently from normal LR
A S g
parsers
goto Q X
2
The b ehaviour of a normal LR parser up on a reduc
closure f A X j A X Q A S g
tion with some rule A is very simple it p ops j j
states from the stack revealing say state Q it then
At each shift where X is some terminal and each re
pushes state goto Q A We identify a state with its
duce with some rule A where X is A we may non
corresp onding set of items
deterministically apply goto which corresp onds with
1
For extended grammars the b ehaviour up on a reduc
case a or goto which corresp onds with case b Of
2
tion cannot b e realised in this way since the regular
course one or b oth may not b e de ned on Q and X
expression of which the rhs is comp osed may describ e
b ecause goto Q X may b e for i f g
i
strings of various lengths so that it is unknown how
Now remark that when using goto and goto each
1 2
many states need to b e p opp ed
reachable set of items contains only items of the form
In this problem is solved by forcing the parser to
A for some xed string plus some nonkernel
decide at each call goto Q X whether
items We will ignore the nonkernel items since they
can b e derived from the kernel items by means of the
a X is one more symbol of an item in Q of which some
closure function
symbols have already b een recognized or whether
This suggests representing each set of items by a new
b X is the rst symbol of an item which has b een
kind of item of the form fA A A g which
1 2 n
introduced in Q by means of the closure function
represents all items A for some and A
In the second case a state which is a variant of
fA A A g Formally
1 2 n
goto Q X is pushed on top of state Q as usual In
ELR
y
I f j fA j A P g
the rst case however state Q on top of the stack is
fS g g
replaced by a variant of goto Q X This is safe since
where we use the symbol to range over sets of non
we will never need to return to Q if after some more
terminals
steps we succeed in recognizing some rule corresp ond
ing with one of the items in Q A consequence of the
Algorithm Extended LR
ELR ELR
action in the rst case is that up on reduction we need
A T I Init Fin Init fS g Fin
to p op only one state o the stack
fS g S and de ned by
Further work in this area is rep orted in which
av a v
treats nondeterministic ELR parsing and therefore do es
y
where fA j A a B C P B
not regard it as an obstacle if a choice b etween cases a
A C g is non empty
and b cannot b e uniquely made
av a v
We are not concerned with extended context free
y
where fA j A a P g is non empty
grammars in this pap er However a very interesting
v A v
algorithm results from ELR parsing if we restrict its ap
y
where there is A P with A and
plication to ordinary context free grammars We will
y
fD j D A B C P B D C g is
maintain the name extended LR to stress the origin
non empty
of the algorithm This results in the new nondetermin
v A v
istic ELR algorithm that we describ e b elow derived
y
where there is A P with A and
from the formulation of ELR parsing in
y
fB j B A P g is non empty
First we de ne a set of items as
Note that Clauses and corresp ond with goto and
y
2
I f A j A P g
that Clauses and corresp ond with goto
1
LC
Note that I I If we de ne for each Q I
Example Consider again the grammar from Exam
ple Using the ELR algorithm recognition of a a is
closure Q
realised by
Q f A j B C Q A C g
fE g a a
fE g fF g a a
then the goto function for LR parsing is de ned by
fE g fT g F a
goto Q X
fE g fT E g T a
fE g fT g T a
closure f A X j A X Qg
For ELR parsing however we need two goto func
tions goto and goto one for kernel items i e those
fE g E
1 2
a a a
Comparing these con gurations with those reached by
a a a
the PLR recognizer we see that here after Step the
F a a
stack element fT E g T represents b oth T T
T a a
F and T T F but also E T and
E a a
E T E so that nondeterminism is even further
E a a
reduced 2
E a a
A simpli ed ELR algorithm which we call the pseudo
E F a
ELR algorithm results from avoiding reference to in
E T a
Clauses and In Clause we then have a simpli ed
E T a
de nition of viz fA j A a B C
E T a
y
P A C g and in the same way we have in Clause
We see that in Step the rst incorrect symbol is read
the new de nition fD j D A B C
but recognition then continues Eventually the recog
y
P D C g Pseudo ELR parsing can b e more easily
nition pro cess is blo cked in some unsuccessful con gu
realised than full ELR parsing but the correct pre x
ration which is guaranteed to happ en for any incorrect
prop erty can no longer b e guaranteed Pseudo ELR
4
input In general however after reading the rst incor
parsing is the foundation of a tabular algorithm in
rect symbol the algorithm may p erform an unbounded
number of steps b efore it halts Imagine what happ ens
Common pre x parsing
for input of the form a a a a a a 2
One of the more complicated asp ects of the ELR algo
rithm is the treatment of the sets of nonterminals in
Tabular parsing
the left hand sides of items A drastically simpli ed
Nondeterministic push down automata can b e realised
algorithm is the basis of a tabular algorithm in
e ciently using parse tables A parse table consists
Since in the algorithm itself is not describ ed but
of sets T of items for i j n where a a
i j 1 n
2
only its tabular realisation we take the lib erty of giv
represents the input The idea is that an item is only
ing this algorithm our own name common pre x CP
stored in a set T if the item represents recognition of
i j
parsing since it treats all rules with a common pre x
the part of the input a a
i+1 j
3
simultaneously
We will rst discuss a tabular form of CP parsing
The simpli cation consists of omitting the sets of
since this is the most simple parsing technique discussed
nonterminals in the left hand sides of items
ab ove We will then move on to the more di cult ELR
CP y
technique Tabular PLR parsing is fairly straightfor
I f j A P g
ward and will not b e discussed in this pap er
Algorithm Common pre x
CP CP
Tabular CP parsing
A T I Init Fin Init Fin S
and de ned by
CP parsing has the following tabular realization
Algorithm Tabular common pre x
av a v
CP
y
Sets T of the table are to b e subsets of I Start
where there are A a B C P such that
i j
with an empty table Add to T Perform one of
A C
0 0
the following steps until no more items can b e added
av a v
y
Add a to T for a a and T
where there is A a P
i 1 i i j i 1
y
where there are A a B C P such that
v A v
y
A C
where there are A D A B C P
such that D Add a to T for a a and T C
j i i j i 1
y
where there is A a P
v A v
y
where there are A B A P
Add A to T for T and T
j i j i h j
y
where there are A D A B C P
The simpli cation which leads to the CP algorithm
such that D C
inevitably causes the correct pre x prop erty to b e lost
Add A to T for T and T
h i j i h j
Example Consider again the grammar from Exam
y
where there are A B A P
ple It is clear that a a a is not a correct string
Rep ort recognition of the input if S T
0 n
according to this grammar The CP algorithm may go
through the following sequence of con gurations
For an example see Figure
Tabular CP parsing is related to a variant of CYK
2
An attempt has b een made in but this pap er do es
parsing with TD ltering in A form of tabular
not describ e the algorithm in its full generality
3 4
The original algorithm in applies an optimization unless the grammar is cyclic in which case the parser
concerning unit rules irrelevant to our discussion may not terminate b oth on correct and on incorrect input
(0) (1) (5)
a E E T
(2)
F E
Consider again the grammar from
(3)
T
Example and the incorrect in
(4)
E
put a a a After execution
of the tabular common pre x al
gorithm the table is as given here
The sets T are given at the j th
(6) (9)
a T T E
j i
row and i th column
(7)
F
The items which corresp ond with
(8)
T
those from Example are lab elled
with These lab els also
indicate the order in which these
(10)
a
items are added to the table
F
T
E
Figure Tabular CP parsing
CP parsing without top down ltering i e without the However for certain i there may b e many
checks concerning the left corner relation T for some j and each may give rise to a di erent is the
j i 1
which is non empty In this way Clause may add main algorithm in
several items a to T some p ossibly with Without the use of top down ltering the references
i 1 i
overlapping sets Since items represent computation to in Clauses and are clearly not of much use
of sub derivations the algorithm may therefore compute any more When we also remove the use of these items
the same sub derivation several times then these clauses b ecome
We prop ose an optimization which makes use of the
Add a to T for a a
i 1 i i
fact that all p ossible items T are already
y
j i 1
where there is A a P
present when we compute items in T we compute
i 1 i
Add A to T for T
j i j i
one single item a where is a large set com
y
where there are A D A P
puted using all T for any j A similar
j i 1
optimization can b e made for the third clause
In the resulting algorithm no set T dep ends on any
i j
set T with g i In this fact is used to construct
g h
Algorithm Tabular extended LR
a parallel parser with n pro cessors P P with
ELR
0 n 1
Sets T of the table are to b e subsets of I Start
i j
each P pro cessing the sets T for all j i The ow
i i j
with an empty table Add fS g to T For
0 0
of data is strictly from right to left i e items computed
i n in this order p erform one of the following
by P are only passed on to P P
i 0 i 1
steps until no more items can b e added
Add a to T for a a
Tabular ELR parsing
i 1 i i
where fA j j T A a B
j i 1
The tabular form of ELR parsing allows an optimiza
y
C P B A C g is non empty
tion which constitutes an interesting example of how a
tabular algorithm can have a prop erty not shared by its
Add a to T for a a and
j i i
5
nondeterministic origin
T
j i 1
y
First note that we can compute the columns of a
where fA j A a P g is non empty
parse table strictly from left to right that is for xed i
Add A to T for T
j i j i
we can compute all sets T b efore we compute the sets
j i
y
where there is A P with A and
T
j i+1
fD j h T D A B C
h j
If we formulate a tabular ELR algorithm in a naive
y
P B D C g is non empty
way analogously to Algorithm as is done in then
Add A to T for T and
for example the rst clause is given by
h i j i
T
h j
Add a to T for a a and
i 1 i i
y
where there is A P with A and
T
j i 1
y
fB j B A P g is non empty
y
where fA j A a B C P B
A Rep ort recognition of the input if fS g S T C g is non empty
0 n
5
Informally the top down ltering in the rst and
This is reminiscent of the admissibility tests which
third clauses is realised by investigating all left corners
are applicable to tabular realisations of logical push down
D of nonterminals C i e D C which are exp ected automata but not to these automata themselves
from a certain input p osition For input p osition i these We conclude that we have a family consisting of LC
nonterminals D are given by PLR ELR and LR parsing which are increasingly de
terministic In general the more deterministic an algo
S fD j j T
i j i
rithm is the more parser states it requires For exam
y
B C P B D C g
ple the LC algorithm requires a number of states the
LC
items in I which is linear in the size of the gram
Provided each set S is computed just after comple
i
mar By contrast the LR algorithm requires a number
tion of the i th column of the table the rst and third
of states the sets of items which is exponential in the
clauses can b e simpli ed to
size of the grammar
Add a to T for a a
i 1 i i
The di erences in the number of states complicates
y
where fA j A a P g S is non empty
i 1
the choice of a tabular algorithm as the one giving op
timal b ehaviour for all grammars If a grammar is very
Add A to T for T
j i j i
y
simple then a sophisticated algorithm such as LR may
where there is A P with A and
y
allow completely deterministic parsing which requires a
fD j D A P g S is non empty
j
linear number of entries to b e added to the parse table
which may lead to more practical implementations
measured in the size of the grammar
Note that we may have that the tabular ELR algo
If on the other hand the grammar is very ambigu
rithm manipulates items of the form which
ous such that even LR parsing is very nondeterministic
would not o ccur in any search path of the nondeter
then the tabular realisation may at worst add each state
ministic ELR algorithm b ecause in general such a
to each set T so that the more states there are the
i j
is the union of many sets of items which
more work the parser needs to do This favours sim
would b e manipulated at the same input p osition by the
ple algorithms such as LC over more sophisticated ones
nondeterministic algorithm in di erent search paths
such as LR Furthermore if more than one state repre
With minor di erences the ab ove tabular ELR algo
sents the same sub derivation then computation of that
rithm is describ ed in A tabular version of pseudo
sub derivation may b e done more than once which leads
ELR parsing is presented in Some useful data
to parse forests compact representations of collections
structures for practical implementation of tabular and
of parse trees which are not optimally dense
non tabular PLR ELR and CP parsing are describ ed
Schabes prop oses to tune a parser to a grammar or
in
in other words to use a combination of parsing tech
niques in order to nd an optimal parser for a certain
Finding an optimal tabular algorithm
7
grammar This idea has until now not b een realised
In Schabes derives the LC algorithm from LR pars
However when we try to nd a single parsing algorithm
ing similar to the way that ELR parsing can b e derived
which p erforms well for all grammars then the tabu
from LR parsing The LC algorithm is obtained by not
lar ELR algorithm we have presented may b e a serious
only splitting up the goto function into goto and goto
1 2
candidate for the following reasons
but also splitting up goto even further so that it non
2
deterministically yields the closure of one single kernel
For all i j and at most one item of the form
item This idea was describ ed earlier in and more
is added to T Therefore identical sub
i j
recently in
derivations are not computed more than once This
Schabes then argues that the LC algorithm can b e
is a consequence of our optimization in Algorithm
determinized i e made more deterministic by manip
Note that this also holds for the tabular CP algo
ulating the goto functions One application of this idea
rithm
is to take a xed grammar and choose di erent goto
ELR parsing guarantees the correct pre x prop erty
functions for di erent parts of the grammar in order
contrary to the CP algorithm This prevents com
to tune the parser to the grammar
putation of all sub derivations which are useless with
In this section we discuss a di erent application of
regard to the already pro cessed input
this idea we consider various goto functions which are
global i e which are the same for all parts of a grammar
ELR parsing is more deterministic than LC and PLR
One example is ELR parsing as its goto function can
2
parsing b ecause it allows shared pro cessing of all
b e seen as a determinized version of the goto function
2
common pre xes It is hard to imagine a practical
of LC parsing In a similar way we obtain PLR parsing
parsing technique more deterministic than ELR pars
Traditional LR parsing is obtained by taking the full
ing which also satis es the previous two prop erties
determinization i e by taking the normal goto function
In particular we argue in that re nement of the
6
which is not split up
LR technique in such a way that the rst prop erty
ab ove holds whould require an impractically large 6
Schabes more or less also argues that LC itself can b e
number of LR states
obtained by determinizing TD parsing In lieu of TD pars
ing he mentions Earley s algorithm which is its tabular
7
realisation This is reminiscent of the idea of optimal cover
M J Nederhof Generalized left corner parsing In Epsilon rules
Sixth Conference of the European Chapter of the
Epsilon rules cause two problems for b ottom up pars
ACL
ing The rst is non termination for simple realisations
of nondeterminism such as backtrack parsing caused
M J Nederhof A multidisciplinary approach to
by hidden left recursion The second problem o ccurs
a parsing algorithm In K Sikkel and A Ni
when we optimize TD ltering e g using the sets S it
jholt editors Natural Language Parsing Methods
i
is no longer p ossible to completely construct a set S b e
and Formalisms Pro c of the sixth Twente Work
i
fore it is used b ecause the computation of a derivation
shop on Language Technology University
deriving the empty string requires S for TD ltering
of Twente
i
but at the same time its result causes new elements to
M J Nederhof and G Satta An extended theory
b e added to S Both problems can b e overcome
i
of head driven parsing In this pro ceedings
P Oude Luttighuis and K Sikkel Generalized LR
Conclusions
parsing and attribute evaluation In Third Inter
We have discussed a range of di erent parsing algo
national Workshop on Parsing Technologies
rithms which have their ro ots in compiler construction
Tilburg The Netherlands and Durbuy Bel
expression parsing and natural language pro cessing
gium August
We have shown that these algorithms can b e describ ed
P W Purdom Jr and C A Brown Parsing
in a common framework
extended LR k grammars Acta Informatica
We further discussed tabular realisations of these al
gorithms and concluded that we have found an opti
mal algorithm which in most cases leads to parse tables
J Rekers Parser Generation for Interactive Envi
containing fewer entries than for other algorithms but
ronments PhD thesis University of Amsterdam
which avoids computing identical sub derivations more
than once
D J Rosenkrantz and P M Lewis I I Deterministic
left corner parsing In IEEE Conference Record
Acknowledgements
of the th Annual Symposium on Switching and
Automata Theory
The author acknowledges valuable corresp ondence with
Klaas Sikkel Ren e Leermakers Fran cois Barth elemy
Y Schabes Polynomial time and space shift
Giorgio Satta Yves Schabes and Fr ed ericVoisin
reduce parsing of arbitrary context free grammars
In th Annual Meeting of the ACL
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