This paper presents an approach that allows the efficient integration of
speech recognition and language understanding using Tomita's generalized
LR-parsing algorithm. For this purpose the GLRP-algorithm is revised so that an
agenda mechanism can be used to control the flow of computation of the parsing
process. This new approach is used to integrate speech recognition and speech
understanding incrementally with a beam search method. These considerations
have been implemented and tested on ten word lattices.Comment: 4 pages, 61K postscript, compressed, uuencoded, Eurospeech 9/95,
  Madri

Staab, Steffen

English

arXiv

The process of understanding spoken language requires the efficient processing of ambiguities that arise by the nature of speech. This paper presents an approach that allows the efficient incremental integration of speech recognition and language understanding using Tomita´s generalized LR-parsing algorithm. For this purpose the GLR-lattice-parsing-algorithm is revised so that an agenda mechanism can be used to control the flow of computation of the parsing process. Subsequently the HMM-evaluations of the word models are combined with a stochastical language model to do a beam search similar to where chartparsers are used to do the job

Scientific documents from the Saarland University,

Verbmobil 
GLR Parsing of Word Lattices 
Using a Beam Search Method 
Steffen Staab 
IMMD VllljUER 
Verbundvorhaben 
Report 127 
1995 
 
Steen Staab
IMMD VIII  Kunstliche Intelligenz
Universitat ErlangenNurnberg
Am Weichselgarten 
D 	 Erlangen
Tel
 
email Staabcolingunifreiburgde
Gehort zum Antragsabschnitt  
 Architektur integrierter Parser fur gesprochene Sprache
Die vorliegende Arbeit wurde im Rahmen des Verbundvorhabens Verbmobil vom Bundesministerium fur Bildung
Wissenschaft Forschung und Technologie BMBF unter dem Forderkennzeichen   IV    H gefordert
 Die
Verantwortung fur den Inhalt dieser Arbeit liegt bei dem Autor

GLRPARSING OF WORD LATTICES USING A BEAM SEARCH METHOD
Steen Staab
email staabcoling
unifreiburg
de
Vorstetter Strae A
  Gundelngen
Germany
ABSTRACT
The process of understanding spoken language re
quires the ecient processing of ambiguities that arise
by the nature of speech
 This paper presents an ap
proach that allows the ecient incremental integra
tion of speech recognition and language understand
ing using Tomitas generalized LRparsing algorithm

For this purpose the GLRlatticeparsingalgorithm
   is revised so that an agenda mechanism can be
used to control the ow of computation of the parsing
process
 Subsequently the HMMevaluations of the
word models are combined with a stochastical lan
guage model to do a beam search similar to     
where chartparsers are used to do the job

 INTRODUCTION
In   M
 Tomita proposes a parsing algorithm Gen
eralized LRParsing GLRP and extends it in    to
an algorithm that can parse whole word lattices
 This
algorithm often works more eciently with grammars
for natural languages than others see   

Nevertheless the latticeGLRP is not very exible and
requires the parse of the whole lattice in a certain or
der
 Therefore it remains impossible to use it in real
size applications that must handle  and more word
hypotheses in each word lattice  in spite of its e
ciency

It is generally acknowledged that the problem regard
ing the size of the word lattices can only be solved by
using heuristics that can guide the parsing process

Typically the following two models are combined an
acoustic model that represents the probability that a
certain word was uttered during a time interval and a
language model e
g
 a probabilistic regular grammar
that scores word sequences

In section  a revised version of the original GLRP
is presented
 This new algorithm consists of three
basic actions that act on the core data structure of
the GLRP the graph structured stack
 They are de
signed in such a way that their instances may be pro
cessed in any random order which makes it possible
to put them into a control data structure agenda
and work them down according to a certain strategy

This means a new quality of control over the order of
processing of a parser that uses LRparsing tables

Also by this way it will be possible in the sections
following to combine the basic actions with a heuris
tic scoring function
 This combination will allow to
guide the search through the lattice in order to nd
the word sequence that has the best evaluation and
its syntactic derivation very fast

 THE REVISED GLRP
First the crucial data structures are dened to be ei
ther sets of some kind or pascallike records
 Vertex Time State LinkSet A Vertex repre
sents a left context
 It can be referenced by its time
and the slrtable state it represents
 Furthermore
it has got a set of links

 Link Node PS A Link is a reference to a node
in the ParseForest that also connects a vertex A
to a set of predecessor vertices PS 
 The slrtable
lookup of the state of these vertices PS together
with the category of Node yields the state of ver
tex A

 Node Cat Start End Hypos or Cat Start
End SubtrSeqs It can be uniquely identied by
the triple Cat Start End
 It either references
a set of word hypotheses  then the category is a
terminal  or a set of sequences of subtrees  then
Cat is nonterminal

 GraphStructured Stack GSS  The GSS is a
set of links and vertices

  Set of Nodes ParseForest  The ParseForest
represents all possible derivations

  Set of Actions Agenda All actions are placed
on the Agenda and are carried out according to
some strategy

  Set of NewHypos OldHypoActions that have al
ready been executed

The new approach does not only lead to a more ex
ible algorithm it also divides the work that has to be
done by the GLRP more concisely into the three main
mechanisms
 
 Shift construct a new element in the GSS  if it
does not already exist

 Search initiate new Shifts with nonterminal cate
gories

 NewHypo initiate new Shifts with terminal cate
gories
The basic actions are
ShiftVertex Node Time State
 
 if V
i
 GSS  st
 V
i
 T
i
 S
i
 LinkSet
i

T
i
 Time and S
i
 State then
if L
j
 LinkSet
i
 st
 L
j
 N
j
 PS
j
 and
N
j
 Node then 
 else 

else 


   if Vertex  PS
j
then return
  add Vertex to PS
j
  assume Vertex   State
l
 LinkSet
l

  for all previous SearchRule
nr
 SubtrSeq Link
EndingTime st
 Link  L
j
do
if jSubtrSeq j  jrightsideRule
nr
j then
add ShiftVertex N
m
 EndingTime
slrtableState
l
 HeadCatRule
nr
~~
to Agenda where N
m
is the node that was
created by the shift action which was initi
ated by this previous search
else
for all links L
k
 N
k
  LinkSet
l
do
add SearchRule
nr
 consN
k
 SubtrSeq
L
k

EndingTime to Agenda
  return

   create link L
j
 Node fVertexg
  for all actions SearchRule
nr
 SubtrSeq
Link st
 Link  PS V
i
 PS and
jSubtrSeq j   jrightsideRule
nr
j do
add SearchRule
nr
 consNode SubtrSeq L
j

to Agenda
  return

   create link L
i
 NodefVertexg
create V
i
 Time State fL
i
g
add L
i
and V
i
to GSS
  for all NewHypoH  OldHypoActions where
H  ST ET K ST  Time
for all categories C
j
that are possible according
to the lexical Key K do
if S
j
 st
  Shift S
j
  slrtableState C
j

then
add ShiftV
i
 N
j
 ET S
j
 to Agenda where
N
j
 C
j
 ST ET
  SentinelLink  fg fV
i
g
  for all categories C
j

for all  Reduce Rule
nr
  slrtableV
i
C
j
 do
add SearchRule
nr
  SentinelLink Time to
Agenda
  return
NewHypoH H  Start End Key
  for all categories C
j
that are possible according to
the lexical key Key do
if N
k
 C
k
 S
k
 E
k
 Hs
k
  ParseForest  such
that C
k
 C
j
 S
k
 Start and E
k
 End  then
 add H to Hs
k
else
 create a node N
j
 C
j
 Start End fHg in
the ParseForest
 for all vertices V
i
 GSS  such that
V
i
 Time
i
 State
i
 Time
i
 Start 
NewState and
 Shift NewState  slrtableState
i
 C
j
 do
add action ShiftV
i
 N
j
 End NewState to
the Agenda
  store NewHypoH in OldHypoActions
  return
SearchRule
nr
 SubtrSeq Link EndingTime
 
 if jSubtrSeq j  jrightsideRule
nr
j then 
 else



 if N
i
 ParseForest  st
N
i
 C
i
 ST
i
 ET
i
 StS
i

HeadCatRule
nr
  C
i
 ST
i
 T
k
 V
k
 T
k

V
k
 PS
l
 Link   PS
l
 ET
i
 EndingTime
then
  add SubtrSeq to StS
i
 return
else
  create a node N
i
 HeadCatRule
nr
 T
k

EndingTime fSubtrSeqg in the Parse
Forest
  for all vertices V
m
 PS  where Link  N PS
V
m
  S
m
 C
i
 HeadCatRule
nr
 do
add ShiftV
m
 N
i
 EndingTime
slrtableS
m
 C
i
~~ to Agenda
  return

   for all V
i
 PS  st
 Link   PS V
i
 
LS
i
 and for all L
j
 LS
i
 where L
j
 N
j

do
add SearchRule
nr
 consN
j
 SubtrSeq L
j

EndingTime to Agenda
  return
The main routine is quite simple
 
 vertex V
 
    GSS  fV
 
g


 initialize the Agenda with one NewHypo action for
each word hypothesis of the lattice

 until there are no more actions on the Agenda do
take one action from the Agenda and carry it out
logP
normal
w j NGram HMM 
 


  logP
normal
w j NGram

logP
normal
w j HMM
 
logP
inside
L 

logP
normal
w j NGram HMM if lengthw  
 if lengthw  

logP
outside
L  max
l linksK 
normalize

B
B

denormalizelogP
outside
l
denormalizelogP
inside
L
  logP first wordLj
last wordlBigram

C
C
A

Besides productions need not be handled seper
ately anymore
 Therefore the Common Lisp code of
an implementation of the revised GLRP has shrunk
about   compared with an implementation of the
original GLRP

An implementation of the beam search agenda GLRP
is available by FTP from faui	
informatik
uni
erlangen
de  !pub!lisp!parser!glrlatticeparser
tar
gz"

Or send email

 WORST CASE BEHAVIOUR OF THE
REVISED GLRP
The exibility of the revised GLRP should not incur
heavy costs on the runtime behaviour
 The crucial
places to look for a decrease in performance compared
to Tomitas GLRP are the steps forloops and ex
istential conditions where some instances vertices
previous search actions etc
 must be retrieved

However each of these steps either has an equiva
lent action in Tomitas GLRP or it can be retrieved
trivially by some additional information that must be
added to the GraphStructured Stack For a thorough
description of the new data structure please refer to

 Therefore the worst case behaviour of the revised
GLRP is of the same order as Tomitas

 BEAM SEARCH
In order to combine the GLRP with heuristic scores it
is necessary to dene the scoring function and bring
arguments why it was chosen

 A Metric For The Beam Search
At least see also   the following design criteria
should be met for the metric
 
 It should combine a bigram model with the acous
tic score of the HMM word models


 Evaluations of dierent actions should be compa
rable


 The complete left context information should be
considered

To ensure the comparability of dierent actions the
probabilities of the bigrammodel and the word model
are normalized
 The normalization of the bigram
model entails a division by the number of operations
that have been applied while the word model proba
bility is divided by the number of time units the word
spans nevertheless this is an adhoc normalization
that must be improved in the long run
logP
normal
wjBigram 
logP wjBigram
#BigramOperation
logP
normal
wjHMM  
logP wjHMM 
#Frames
Since both schemes are often not drawn from the
same test sample and are seldom really equally impor
tant it is useful to combine them with an adjustment
parameter  eq
  
 The value of this parameter
 can be found by experiments or an optimization
procedure

For the purpose of encorporating the left context
probability the evaluations are partitioned in inside
evaluations and outside evaluations

Furthermore they are dened on the corresponding
links instead of the respective word sequences be
cause the same word sequence may be a continuation
of dierent left contexts and the respective probabil
ities under these dierent conditions may vary
 I
e

that dierent links may have the same or dierent
nodes that cover the same word sequence
 The left
context of a link can easily be identied by its set of
predecessor vertices

The inside evaluation of a link L with a node cov
ering the word sequence w is given by equation 

The outside evaluation of a link L with predecessor
vertex K and a bigram model is dened recursively
by eq
 
 If K is the start vertex then in eq
 
 logP
outside
l" must be substituted by  " and the
 last wordl" by  $BEGINMARKER$"

The function denormalize causes an extraction of the
acoustic and the ngram score and undoes the normal
ization over the respective length
 This is necessary
since the normalized scores can not be combined di
rectly
 normalize is the corresponding inverse func
tion

If a link has a node that spans several word sequences
a maximization over all sequences must be done since
the best analysis is wanted

 Integrating The Beam Search Into The
Revised GLRP
In the implemented version the Shift actions are
scored according to the outside evaluation of the new
link
 Of course also the other two types of action
could be scored and worked down according to their
scores
 But for reasons of simplicity and since most
Search actions only act along paths with good evalu
ations  almost these alone are constructed by the
Shift actions  the Search actions and the NewHypo
actions are handled with a stack that has a higher
priority than the Shift actions

The beam search strategy itself consists out of two
stages
 
 The algorithm works through the lattice time in
crementally
 Thereby it evaluates all possible actions
during each time frame but processes only those the
score of which is within a beam around the best
current score
 All other actions are saved onto the
 PrunedAgenda"


 If a parse could not be found during stage   the ac
tions that were saved onto the  PrunedAgenda" are
processed with a best rst search

	 EXPERIMENTS
Tests were carried out with a slrtable of a  % rules
CFG
 Ten word lattices where word hypotheses fam
ilies were already reduced to single word hypothe
ses and those single hypotheses numbered between %
and  were parsed with the described beam search
strategy
 In combination with the acoustic scores
from the decoder a bigram model with rather high
perplexity   was used to guide the search
 Un
der these conditions 	 of the lattices could be han
dled successfully and with one exception the parsing
of the recognized structures took less than  seconds


 RELATED WORK
There have been various systems that employ stochas
tic control dierent strategies and  more rarely
 GLRParsing techniques
 E
g
 Shikano 	 shows
how to use ngram models
 Paseler et
 al
  pub
lished a beam search method
 This method is com
bined with a ngram model by Paseler and Ney 

Wrigley and Wright e
g
   use a probabilistic CFG
as their language model
 In % best rst search is
demonstrated by T
 Sene
 In H
 Ney   sets of
phoneme hypotheses are analysed with a beam search
strategy and the use of ngram models in this context
is explained
 L
 Schmid uses the A$algorithm to do a
best rst search over the number of word hypotheses
in 
 Etc

However none of them presents a general approach to
guide the GLRparsing process with stochastic infor
mation and especially to combine GLRparsing with
a beam search strategy

 CONCLUSION
In this paper a revised version of Tomitas GLR
parsing algorithm is described that allows the exible
use of strategies
 It is combined with a beam search
strategy to parse word lattices and return a packed
forest representation of a number of parse trees with
good scores
 While theoretical considerations show
that the worst case behaviour of the revised algorithm
is of the same order as Tomitas original algorithm
the experiments demonstrate that the new algorithm
might be used in nontrivial applications

The experiments also indicate that GLRP itself is use
ful
 E
g
 Schabes  argues that GLRP was heavily
handicapped because the number of slrtable states
could be exponential to the number of CFG rules

However the  % rules CFG that is used in the ex
periments generates only ca
  states
 This sup
ports Tomitas claim that grammars for natural lan
guages were not too densely ambiguous and therefore
GLRP was appropriate for natural language parsing

Acknowledgements
This research is part of the authors Masters thesis

It was done at the department of computer science
VIII AI University of Erlangen and encouraged by
my advisor Mark Steedman University of Pennsylva
nia
 I would like to thank Hans Weber for many fruit
ful discussions and Gunther Gorz and Angela Rosch
for helpful comments on the paper

References
  H
 Ney
 Architecture and search strategies for
largevocabulary continuousspeech recognition

In NATOASI BUBI

ON pages   	  

 A
 Paseler and H
 Ney
 Continuousspeech recog
nition using a stochastic language model
 In
ICASSP  	

 A
 Paseler H
 Ney and et al
 A data driven
organization of the dynamic programming beam
search for continuous speech recognition
 In
ICASSP  	

 Y
 Schabes
 Polynomial time and space shift
reduce parsing
 In Proc 	
th Annual Meeting of
the Assoc for Computational Linguistics pages
 %       

 L
 Schmid
 Parsing word graphs using a linguis
tic grammar and a statistical language model
 In
ICASSP pages II    II  August  

% S
 Sene
 TINA a probabilistic syntactic parser

In ICASSP  	

 P
 Shann
 Experiments with GLR and chart pars
ing
 In M
 Tomita editor Generalized LR Pars
ing pages  
 Kluwer Academic Publishers
  

	K
 Shikano
 Improvement of word recognition re
sults by trigram model
 In ICASSP  	

 S
 Staab
 GLRparsing of word lattices
 Masters
thesis University of Pennsylvania  

 M
 Tomita
Ecient parsing for natural language

Kluwer  	

  M
 Tomita
 An ecient word lattice parsing algo
rithm
 In ICASSP pages     August  	%

  H
 Weber
 LRinkrementelles probabilistis
ches Chartparsing von Worthypothesenmengen
mit Unikationsgrammatiken
 PhD thesis Univ

Hamburg  

  E
 N
 Wrigley and J
 H
 Wright
 Computa
tional requirements of probabilistic LR parsing
for speech recognition
 In Proc Eurospeech 

  



GLR parsing of word lattices using a beam search method

Universaar

Acronym

Verbmobil GLR Parsing of Word Lattices Using a Beam Search Method Steffen Staab IMMD VllljUER Verbundvorhaben Report 127 1995  Steen StaabIMMD VIII  Kunstliche IntelligenzUniversitat ErlangenNurnbergAm Weichselgarten D 	 ErlangenTel email StaabcolingunifreiburgdeGehort zum Antragsabschnitt   Architektur integrierter Parser fur gesprochene SpracheDie vorliegende Arbeit wurde im Rahmen des Verbundvorhabens Verbmobil vom Bundesministerium fur BildungWissenschaft Forschung und Technologie BMBF unter dem Forderkennzeichen   IV    H gefordert DieVerantwortung fur den Inhalt dieser Arbeit liegt bei dem AutorGLRPARSING OF WORD LATTICES USING A BEAM SEARCH METHODSteen Staabemail staabcolingunifreiburgdeVorstetter Strae A  GundelngenGermanyABSTRACTThe process of understanding spoken language requires the ecient processing of ambiguities that ariseby the nature of speech This paper presents an approach that allows the ecient incremental integration of speech recognition and language understanding using Tomitas generalized LRparsing algorithmFor this purpose the GLRlatticeparsingalgorithm   is revised so that an agenda mechanism can beused to control the ow of computation of the parsingprocess Subsequently the HMMevaluations of theword models are combined with a stochastical language model to do a beam search similar to     where chartparsers are used to do the job INTRODUCTIONIn   M Tomita proposes a parsing algorithm Generalized LRParsing GLRP and extends it in    toan algorithm that can parse whole word lattices Thisalgorithm often works more eciently with grammarsfor natural languages than others see   Nevertheless the latticeGLRP is not very exible andrequires the parse of the whole lattice in a certain order Therefore it remains impossible to use it in realsize applications that must handle  and more wordhypotheses in each word lattice  in spite of its eciencyIt is generally acknowledged that the problem regarding the size of the word lattices can only be solved byusing heuristics that can guide the parsing processTypically the following two models are combined anacoustic model that represents the probability that acertain word was uttered during a time interval and alanguage model eg a probabilistic regular grammarthat scores word sequencesIn section  a revised version of the original GLRPis presented This new algorithm consists of threebasic actions that act on the core data structure ofthe GLRP the graph structured stack They are designed in such a way that their instances may be processed in any random order which makes it possibleto put them into a control data structure agendaand work them down according to a certain strategyThis means a new quality of control over the order ofprocessing of a parser that uses LRparsing tablesAlso by this way it will be possible in the sectionsfollowing to combine the basic actions with a heuristic scoring function This combination will allow toguide the search through the lattice in order to ndthe word sequence that has the best evaluation andits syntactic derivation very fast THE REVISED GLRPFirst the crucial data structures are dened to be either sets of some kind or pascallike records Vertex Time State LinkSet A Vertex represents a left context It can be referenced by its timeand the slrtable state it represents Furthermoreit has got a set of links Link Node PS A Link is a reference to a nodein the ParseForest that also connects a vertex Ato a set of predecessor vertices PS  The slrtablelookup of the state of these vertices PS togetherwith the category of Node yields the state of vertex A Node Cat Start End Hypos or Cat StartEnd SubtrSeqs It can be uniquely identied bythe triple Cat Start End It either referencesa set of word hypotheses  then the category is aterminal  or a set of sequences of subtrees  thenCat is nonterminal GraphStructured Stack GSS  The GSS is aset of links and vertices  Set of Nodes ParseForest  The ParseForestrepresents all possible derivations  Set of Actions Agenda All actions are placedon the Agenda and are carried out according tosome strategy  Set of NewHypos OldHypoActions that have already been executedThe new approach does not only lead to a more exible algorithm it also divides the work that has to bedone by the GLRP more concisely into the three mainmechanisms  Shift construct a new element in the GSS  if itdoes not already exist Search initiate new Shifts with nonterminal categories NewHypo initiate new Shifts with terminal categoriesThe basic actions areShiftVertex Node Time State  if Vi GSS  st Vi Ti Si LinkSetiTi Time and Si State thenif Lj LinkSeti st Lj Nj PSj andNj Node then  else else    if Vertex  PSjthen return  add Vertex to PSj  assume Vertex   Statel LinkSetl  for all previous SearchRulenr SubtrSeq LinkEndingTime st Link  Ljdoif jSubtrSeq j  jrightsideRulenrj thenadd ShiftVertex Nm EndingTimeslrtableStatel HeadCatRulenr~~to Agenda where Nmis the node that wascreated by the shift action which was initiated by this previous searchelsefor all links Lk Nk  LinkSetldoadd SearchRulenr consNk SubtrSeqLkEndingTime to Agenda  return   create link Lj Node fVertexg  for all actions SearchRulenr SubtrSeqLink st Link  PS Vi PS andjSubtrSeq j   jrightsideRulenrj doadd SearchRulenr consNode SubtrSeq Ljto Agenda  return   create link Li NodefVertexgcreate Vi Time State fLigadd Liand Vito GSS  for all NewHypoH  OldHypoActions whereH  ST ET K ST  Timefor all categories Cjthat are possible accordingto the lexical Key K doif Sj st  Shift Sj  slrtableState Cjthenadd ShiftVi Nj ET Sj to Agenda whereNj Cj ST ET  SentinelLink  fg fVig  for all categories Cjfor all  Reduce Rulenr  slrtableViCj doadd SearchRulenr  SentinelLink Time toAgenda  returnNewHypoH H  Start End Key  for all categories Cjthat are possible according tothe lexical key Key doif Nk Ck Sk Ek Hsk  ParseForest  suchthat Ck Cj Sk Start and Ek End  then add H to Hskelse create a node Nj Cj Start End fHg inthe ParseForest for all vertices Vi GSS  such thatVi Timei Statei Timei Start NewState and Shift NewState  slrtableStatei Cj doadd action ShiftVi Nj End NewState tothe Agenda  store NewHypoH in OldHypoActions  returnSearchRulenr SubtrSeq Link EndingTime  if jSubtrSeq j  jrightsideRulenrj then  else if Ni ParseForest  stNi Ci STi ETi StSiHeadCatRulenr  Ci STi Tk Vk TkVk PSl Link   PSl ETi EndingTimethen  add SubtrSeq to StSi returnelse  create a node Ni HeadCatRulenr TkEndingTime fSubtrSeqg in the ParseForest  for all vertices Vm PS  where Link  N PSVm  Sm Ci HeadCatRulenr doadd ShiftVm Ni EndingTimeslrtableSm Ci~~ to Agenda  return   for all Vi PS  st Link   PS Vi LSi and for all Lj LSi where Lj Njdoadd SearchRulenr consNj SubtrSeq LjEndingTime to Agenda  returnThe main routine is quite simple  vertex V     GSS  fV g initialize the Agenda with one NewHypo action foreach word hypothesis of the lattice until there are no more actions on the Agenda dotake one action from the Agenda and carry it outlogPnormalw j NGram HMM    logPnormalw j NGramlogPnormalw j HMM logPinsideL logPnormalw j NGram HMM if lengthw   if lengthw  logPoutsideL  maxl linksK normalizeBBdenormalizelogPoutsideldenormalizelogPinsideL  logP first wordLjlast wordlBigramCCABesides productions need not be handled seperately anymore Therefore the Common Lisp code ofan implementation of the revised GLRP has shrunkabout   compared with an implementation of theoriginal GLRPAn implementation of the beam search agenda GLRPis available by FTP from faui	informatikunierlangende  !pub!lisp!parser!glrlatticeparsertargz"Or send email WORST CASE BEHAVIOUR OF THEREVISED GLRPThe exibility of the revised GLRP should not incurheavy costs on the runtime behaviour The crucialplaces to look for a decrease in performance comparedto Tomitas GLRP are the steps forloops and existential conditions where some instances verticesprevious search actions etc must be retrievedHowever each of these steps either has an equivalent action in Tomitas GLRP or it can be retrievedtrivially by some additional information that must beadded to the GraphStructured Stack For a thoroughdescription of the new data structure please refer to Therefore the worst case behaviour of the revisedGLRP is of the same order as Tomitas BEAM SEARCHIn order to combine the GLRP with heuristic scores itis necessary to dene the scoring function and bringarguments why it was chosen A Metric For The Beam SearchAt least see also   the following design criteriashould be met for the metric  It should combine a bigram model with the acoustic score of the HMM word models Evaluations of dierent actions should be comparable The complete left context information should beconsideredTo ensure the comparability of dierent actions theprobabilities of the bigrammodel and the word modelare normalized The normalization of the bigrammodel entails a division by the number of operationsthat have been applied while the word model probability is divided by the number of time units the wordspans nevertheless this is an adhoc normalizationthat must be improved in the long runlogPnormalwjBigram logP wjBigram#BigramOperationlogPnormalwjHMM  logP wjHMM #FramesSince both schemes are often not drawn from thesame test sample and are seldom really equally important it is useful to combine them with an adjustmentparameter  eq   The value of this parameter can be found by experiments or an optimizationprocedureFor the purpose of encorporating the left contextprobability the evaluations are partitioned in insideevaluations and outside evaluationsFurthermore they are dened on the correspondinglinks instead of the respective word sequences because the same word sequence may be a continuationof dierent left contexts and the respective probabilities under these dierent conditions may vary Iethat dierent links may have the same or dierentnodes that cover the same word sequence The leftcontext of a link can easily be identied by its set ofpredecessor verticesThe inside evaluation of a link L with a node covering the word sequence w is given by equation The outside evaluation of a link L with predecessorvertex K and a bigram model is dened recursivelyby eq  If K is the start vertex then in eq  logPoutsidel" must be substituted by  " and the last wordl" by  $BEGINMARKER$"The function denormalize causes an extraction of theacoustic and the ngram score and undoes the normalization over the respective length This is necessarysince the normalized scores can not be combined directly normalize is the corresponding inverse functionIf a link has a node that spans several word sequencesa maximization over all sequences must be done sincethe best analysis is wanted Integrating The Beam Search Into TheRevised GLRPIn the implemented version the Shift actions arescored according to the outside evaluation of the newlink Of course also the other two types of actioncould be scored and worked down according to theirscores But for reasons of simplicity and since mostSearch actions only act along paths with good evaluations  almost these alone are constructed by theShift actions  the Search actions and the NewHypoactions are handled with a stack that has a higherpriority than the Shift actionsThe beam search strategy itself consists out of twostages  The algorithm works through the lattice time incrementally Thereby it evaluates all possible actionsduring each time frame but processes only those thescore of which is within a beam around the bestcurrent score All other actions are saved onto the PrunedAgenda" If a parse could not be found during stage   the actions that were saved onto the  PrunedAgenda" areprocessed with a best rst search	 EXPERIMENTSTests were carried out with a slrtable of a  % rulesCFG Ten word lattices where word hypotheses families were already reduced to single word hypotheses and those single hypotheses numbered between %and  were parsed with the described beam searchstrategy In combination with the acoustic scoresfrom the decoder a bigram model with rather highperplexity   was used to guide the search Under these conditions 	 of the lattices could be handled successfully and with one exception the parsingof the recognized structures took less than  seconds RELATED WORKThere have been various systems that employ stochastic control dierent strategies and  more rarely GLRParsing techniques Eg Shikano 	 showshow to use ngram models Paseler et al  published a beam search method This method is combined with a ngram model by Paseler and Ney Wrigley and Wright eg   use a probabilistic CFGas their language model In % best rst search isdemonstrated by T Sene In H Ney   sets ofphoneme hypotheses are analysed with a beam searchstrategy and the use of ngram models in this contextis explained L Schmid uses the A$algorithm to do abest rst search over the number of word hypothesesin  EtcHowever none of them presents a general approach toguide the GLRparsing process with stochastic information and especially to combine GLRparsing witha beam search strategy CONCLUSIONIn this paper a revised version of Tomitas GLRparsing algorithm is described that allows the exibleuse of strategies It is combined with a beam searchstrategy to parse word lattices and return a packedforest representation of a number of parse trees withgood scores While theoretical considerations showthat the worst case behaviour of the revised algorithmis of the same order as Tomitas original algorithmthe experiments demonstrate that the new algorithmmight be used in nontrivial applicationsThe experiments also indicate that GLRP itself is useful Eg Schabes  argues that GLRP was heavilyhandicapped because the number of slrtable statescould be exponential to the number of CFG rulesHowever the  % rules CFG that is used in the experiments generates only ca  states This supports Tomitas claim that grammars for natural languages were not too densely ambiguous and thereforeGLRP was appropriate for natural language parsingAcknowledgementsThis research is part of the authors Masters thesisIt was done at the department of computer scienceVIII AI University of Erlangen and encouraged bymy advisor Mark Steedman University of Pennsylvania I would like to thank Hans Weber for many fruitful discussions and Gunther Gorz and Angela Roschfor helpful comments on the paperReferences  H Ney Architecture and search strategies forlargevocabulary continuousspeech recognitionIn NATOASI BUBION pages   	   A Paseler and H Ney Continuousspeech recognition using a stochastic language model InICASSP  	 A Paseler H Ney and et al A data drivenorganization of the dynamic programming beamsearch for continuous speech recognition InICASSP  	 Y Schabes Polynomial time and space shiftreduce parsing In Proc 	th Annual Meeting ofthe Assoc for Computational Linguistics pages %        L Schmid Parsing word graphs using a linguistic grammar and a statistical language model InICASSP pages II    II  August  % S Sene TINA a probabilistic syntactic parserIn ICASSP  	 P Shann Experiments with GLR and chart parsing In M Tomita editor Generalized LR Parsing pages   Kluwer Academic Publishers  	K Shikano Improvement of word recognition results by trigram model In ICASSP  	 S Staab GLRparsing of word lattices Mastersthesis University of Pennsylvania   M TomitaEcient parsing for natural languageKluwer  	  M Tomita An ecient word lattice parsing algorithm In ICASSP pages     August  	%  H Weber LRinkrementelles probabilistisches Chartparsing von Worthypothesenmengenmit Unikationsgrammatiken PhD thesis UnivHamburg    E N Wrigley and J H Wright Computational requirements of probabilistic LR parsingfor speech recognition In Proc Eurospeech   

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GLR-Parsing of Word Lattices Using a Beam Search Method

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