This is TeX, Version 3.14159 (preloaded format=LaTeX 2002.3.12)  27 JAN 2003 12:12
**&LaTeX rta03subJG.tex
(rta03subJG.tex
LaTeX2e <2001/06/01>
(llncs.cls
Document Class: llncs 2002/01/28 v2.13 
 LaTeX document class for Lecture Notes in Computer Science
(:TeX:Inputs:LaTeX:base:article.cls
Document Class: article 2001/04/21 v1.4e Standard LaTeX document class
(:TeX:Inputs:LaTeX:base:size10.clo
File: size10.clo 2001/04/21 v1.4e Standard LaTeX file (size option)
)
\c@part=\count79
\c@section=\count80
\c@subsection=\count81
\c@subsubsection=\count82
\c@paragraph=\count83
\c@subparagraph=\count84
\c@figure=\count85
\c@table=\count86
\abovecaptionskip=\skip41
\belowcaptionskip=\skip42
\bibindent=\dimen102
) (:TeX:Inputs:LaTeX:tools:multicol.sty
Package: multicol 2000/07/10 v1.5z multicolumn formatting (FMi)
\c@tracingmulticols=\count87
\mult@box=\box26
\multicol@leftmargin=\dimen103
\c@unbalance=\count88
\c@collectmore=\count89
\doublecol@number=\count90
\multicoltolerance=\count91
\multicolpretolerance=\count92
\full@width=\dimen104
\page@free=\dimen105
\premulticols=\dimen106
\postmulticols=\dimen107
\multicolsep=\skip43
\multicolbaselineskip=\skip44
\partial@page=\box27
\last@line=\box28
\mult@rightbox=\box29
\mult@grightbox=\box30
\mult@gfirstbox=\box31
\mult@firstbox=\box32
\@tempa=\box33
\@tempa=\box34
\@tempa=\box35
\@tempa=\box36
\@tempa=\box37
\@tempa=\box38
\@tempa=\box39
\@tempa=\box40
\@tempa=\box41
\@tempa=\box42
\@tempa=\box43
\@tempa=\box44
\@tempa=\box45
\@tempa=\box46
\@tempa=\box47
\@tempa=\box48
\@tempa=\box49
\c@columnbadness=\count93
\c@finalcolumnbadness=\count94
\last@try=\dimen108
\multicolovershoot=\dimen109
\multicolundershoot=\dimen110
\mult@nat@firstbox=\box50
\colbreak@box=\box51
)
\c@chapter=\count95
LaTeX Font Info:    Redeclaring math symbol \Gamma on input line 360.
LaTeX Font Info:    Redeclaring math symbol \Delta on input line 361.
LaTeX Font Info:    Redeclaring math symbol \Theta on input line 362.
LaTeX Font Info:    Redeclaring math symbol \Lambda on input line 363.
LaTeX Font Info:    Redeclaring math symbol \Xi on input line 364.
LaTeX Font Info:    Redeclaring math symbol \Pi on input line 365.
LaTeX Font Info:    Redeclaring math symbol \Sigma on input line 366.
LaTeX Font Info:    Redeclaring math symbol \Upsilon on input line 367.
LaTeX Font Info:    Redeclaring math symbol \Phi on input line 368.
LaTeX Font Info:    Redeclaring math symbol \Psi on input line 369.
LaTeX Font Info:    Redeclaring math symbol \Omega on input line 370.
\tocchpnum=\dimen111
\tocsecnum=\dimen112
\tocsectotal=\dimen113
\tocsubsecnum=\dimen114
\tocsubsectotal=\dimen115
\tocsubsubsecnum=\dimen116
\tocsubsubsectotal=\dimen117
\tocparanum=\dimen118
\tocparatotal=\dimen119
\tocsubparanum=\dimen120
\@tempcntc=\count96
\fnindent=\dimen121
\c@@inst=\count97
\c@@auth=\count98
\c@auco=\count99
\instindent=\dimen122
\authrun=\box52
\authorrunning=\toks14
\tocauthor=\toks15
\titrun=\box53
\titlerunning=\toks16
\toctitle=\toks17
\c@theorem=\count100
\c@case=\count101
\c@conjecture=\count102
\c@corollary=\count103
\c@definition=\count104
\c@example=\count105
\c@exercise=\count106
\c@lemma=\count107
\c@note=\count108
\c@problem=\count109
\c@property=\count110
\c@proposition=\count111
\c@question=\count112
\c@solution=\count113
\c@remark=\count114
\headlineindent=\dimen123
)
(:TeX:Inputs:LaTeX:base:latexsym.sty
Package: latexsym 1998/08/17 v2.2e Standard LaTeX package (lasy symbols)
\symlasy=\mathgroup4
LaTeX Font Info:    Overwriting symbol font `lasy' in version `bold'
(Font)                  U/lasy/m/n --> U/lasy/b/n on input line 42.
) (:TeX:Inputs:LaTeX:graphics:graphicx.sty
Package: graphicx 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR)

(:TeX:Inputs:LaTeX:graphics:keyval.sty
Package: keyval 1999/03/16 v1.13 key=value parser (DPC)
\KV@toks@=\toks18
)
(:TeX:Inputs:LaTeX:graphics:graphics.sty
Package: graphics 2001/07/07 v1.0n Standard LaTeX Graphics (DPC,SPQR)
 (:TeX:Inputs:LaTeX:graphics:trig.sty
Package: trig 1999/03/16 v1.09 sin cos tan (DPC)
)
(:TeX:Inputs:LaTeX:graphics:graphics.cfg
File: graphics.cfg 2001/08/31 v1.1 graphics configuration of teTeX/TeXLive
)
Package graphics Info: Driver file: dvips.def on input line 80.
 (:TeX:Inputs:LaTeX:graphics:dvips.def
File: dvips.def 1999/02/16 v3.0i Driver-dependant file (DPC,SPQR)
))
\Gin@req@height=\dimen124
\Gin@req@width=\dimen125
) (:User:TeX-Inputs:diagrams.tex
<Paul Taylor's commutative diagrams, version 3.88, September 2000>
\CD@uA=\count115
\CD@vA=\count116
\CD@wA=\count117
\CD@xA=\count118
\CD@OA=\dimen126
\CD@PA=\dimen127
\CD@RA=\dimen128
\CD@SA=\dimen129
\CD@yA=\count119
\CD@zA=\count120
\CD@QA=\dimen130
\CD@DA=\box54
\CD@LH=\count121
\CD@TC=\count122
\CD@XH=\dimen131
\CD@zC=\dimen132
\CD@@I=\dimen133
\CD@LF=\dimen134
\CD@oI=\dimen135
\CD@DC=\dimen136
\CD@eJ=\dimen137
\PileSpacing=\dimen138
\CD@nA=\dimen139
\CD@YB=\dimen140
\DiagramCellHeight=\dimen141
\DiagramCellWidth=\dimen142
\MapShortFall=\dimen143
\CD@iA=\dimen144
\rh+:>=\box55
\rt+:<=\box56
\dh+:>=\box57
\dt+:<=\box58
\rt+:>=\box59
\rh+:<=\box60
\dt+:>=\box61
\dh+:<=\box62
\CD@VE=\toks19
\CD@SE=\toks20
\CD@VA=\count123
\CD@ME=\toks21
\CD@XE=\toks22
\CD@RE=\toks23
\CD@TE=\toks24
\CD@QE=\toks25
\CD@WE=\toks26
\CD@OE=\toks27
\CD@PE=\toks28
\CD@NE=\toks29
\CD@UE=\toks30
\CD@CA=\count124
\CD@XB=\count125
\CD@NB=\count126
\CD@FA=\count127
\CD@lA=\count128
\CD@MB=\count129
\CD@GB=\count130
\CD@KG=\box63
\CD@IG=\box64
\DiagonalChoice=\count131
\objectheight=\dimen145
\objectwidth=\dimen146
\CD@NA=\toks31
\CD@xI=\toks32
\CD@lH=\toks33
\CD@hD=\toks34
\CD@hH=\toks35
LaTeX Font Info:    External font `cmex10' loaded for size
(Font)              <7> on input line 1880.
LaTeX Font Info:    External font `cmex10' loaded for size
(Font)              <5> on input line 1880.
LaTeX Font Info:    Try loading font information for U+lasy on input line 1880.


(:TeX:Inputs:LaTeX:base:ulasy.fd
File: ulasy.fd 1998/08/17 v2.2e LaTeX symbol font definitions
)) (rta03subJG.aux)
LaTeX Font Info:    Checking defaults for OML/cmm/m/it on input line 26.
LaTeX Font Info:    ... okay on input line 26.
LaTeX Font Info:    Checking defaults for T1/cmr/m/n on input line 26.
LaTeX Font Info:    ... okay on input line 26.
LaTeX Font Info:    Checking defaults for OT1/cmr/m/n on input line 26.
LaTeX Font Info:    ... okay on input line 26.
LaTeX Font Info:    Checking defaults for OMS/cmsy/m/n on input line 26.
LaTeX Font Info:    ... okay on input line 26.
LaTeX Font Info:    Checking defaults for OMX/cmex/m/n on input line 26.
LaTeX Font Info:    ... okay on input line 26.
LaTeX Font Info:    Checking defaults for U/cmr/m/n on input line 26.
LaTeX Font Info:    ... okay on input line 26.
\c@thm=\count132
LaTeX Font Info:    External font `cmex10' loaded for size
(Font)              <9> on input line 351.
LaTeX Font Info:    External font `cmex10' loaded for size
(Font)              <6> on input line 351.

Overfull \hbox (1.18257pt too wide) in paragraph at lines 380--407
\OT1/cmr/m/n/10 Berry and L^^Sevy [[]] were the first who tried to base al-ge-b
raic se-man-tics [[]]
 []

[1

] [2] [3]
File: reg_order.eps Graphic file (type eps)
 <reg_order.eps> [4] [5]
Underfull \hbox (badness 10000) in paragraph at lines 766--769

 []

[6]
Overfull \hbox (19.08801pt too wide) in paragraph at lines 880--881
\OT1/cmr/m/n/10 let $\OML/cmm/m/it/10 t \OT1/cmr/m/n/10 = \OML/cmm/m/it/10 g\OT
1/cmr/m/n/10 (\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 g\OT1/cmr/m/n
/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 )))$, let $\OML/cmm/m/it/10 P \OT1/cmr/m
/n/10 : \OML/cmm/m/it/10 t \OMS/cmsy/m/n/10 ! \OML/cmm/m/it/10 h\OT1/cmr/m/n/10
 (\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 (\OML/cm
m/m/it/10 x\OT1/cmr/m/n/10 ))\OML/cmm/m/it/10 ; E\OT1/cmr/m/n/10 (\OML/cmm/m/it
/10 g\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1
/cmr/m/n/10 )))) \OMS/cmsy/m/n/10 !$ $\OML/cmm/m/it/10 h\OT1/cmr/m/n/10 (\OML/c
mm/m/it/10 g\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 h\OT1/cmr/m/n/10 (\OML/cmm/m/it/1
0 x; E\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 )))\OML/cmm/m/it/10 ; 
E\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 g\OT1/cmr
/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ))))$,
 []

[7]
Overfull \hbox (1.72993pt too wide) in paragraph at lines 1021--1025
[]\OT1/cmr/m/n/10 Let $\OMS/cmsy/m/n/10 S$ \OT1/cmr/m/n/10 be a reg-u-lar sta-b
le se-man-tics of an SDRS $\OMS/cmsy/m/n/10 R$\OT1/cmr/m/n/10 . Then $\OMS/cmsy
/m/n/10 L[]\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 R\OT1/cmr/m/n/10 )$
 []

[8] [9]
Overfull \hbox (4.54265pt too wide) in paragraph at lines 1182--1187
\OT1/cmr/m/n/10 any SDRS con-sists of (iso-mor-phic copies) of pro-jec-tions of
 its comma-(sub)SDRSs. 
 []


Overfull \hbox (35.9373pt too wide) in paragraph at lines 1205--1210
\OT1/cmr/m/n/10 and $[][][][]$ in $\OMS/cmsy/m/n/10 R[]$\OT1/cmr/m/n/10 . Then 
for any $\OMS/cmsy/m/n/10 S$\OT1/cmr/m/n/10 -needed $\OML/cmm/m/it/10 v[] \OMS/
cmsy/m/n/10 2 \OML/cmm/m/it/10 v=u$\OT1/cmr/m/n/10 , $[][][][]$
 []

[10]
Overfull \hbox (17.53471pt too wide) in paragraph at lines 1313--1319
[]\OT1/cmr/m/n/10 Let $\OMS/cmsy/m/n/10 R \OT1/cmr/m/n/10 = (\OML/cmm/m/it/10 T
er; \OMS/cmsy/m/n/10 !\OML/cmm/m/it/10 ; =\OT1/cmr/m/n/10 )$ be a good SDRS. Th
en $\OMS/cmsy/m/n/10 L[]\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 R\OT1/cmr/m/n/10 ) = 
(\OMS/cmsy/m/n/10 L[]\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 R\OT1/cmr/m/n/10 )\OML/c
mm/m/it/10 ; \U/lasy/m/n/10 ^^B[]\OT1/cmr/m/n/10 )$
 []

[11] [12]
Overfull \hbox (22.63145pt too wide) in paragraph at lines 1425--1430
[]\OT1/cmr/m/n/10 Let $\OMS/cmsy/m/n/10 ^^T \OT1/cmr/m/n/10 = (\OML/cmm/m/it/10
 D; \OMS/cmsy/m/n/10 ^^T[]\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 t[]\OML/cmm/m/it/
10 ; \OMS/cmsy/m/n/10 u[]\OT1/cmr/m/n/10 )$ be a CRD, let $[\OML/cmm/m/it/10 e[
][][]e[][][] [] [][]e[]\OT1/cmr/m/n/10 ]$,
 []

LaTeX Font Info:    External font `cmex10' loaded for size
(Font)              <12> on input line 1482.
LaTeX Font Info:    External font `cmex10' loaded for size
(Font)              <8> on input line 1482.
LaTeX Font Info:    Font shape `U/lasy/b/n' in size <8> not available
(Font)              Font shape `U/lasy/m/n' tried instead on input line 1482.
LaTeX Font Info:    Font shape `U/lasy/b/n' in size <6> not available
(Font)              Font shape `U/lasy/m/n' tried instead on input line 1482.

Overfull \hbox (12.83359pt too wide) in paragraph at lines 1494--1507
\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 F\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 S\OT1/cm
r/m/n/10 )$ onto $\OMS/cmsy/m/n/10 F[] \OT1/cmr/m/n/10 = (\OMS/cmsy/m/n/10 R[]\
OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 '[]\OT1/cmr/m/n/10 )$, where $\OML/cmm/m/it/
10 v[] \OMS/cmsy/m/n/10 '[] \OML/cmm/m/it/10 w[]$ \OT1/cmr/m/n/10 iff $\OML/cmm
/m/it/10 Pv \OMS/cmsy/m/n/10 ' \OML/cmm/m/it/10 Qw$\OT1/cmr/m/n/10 , and $\OML/
cmm/m/it/10 v[] \OT1/cmr/m/n/10 = ([]\OML/cmm/m/it/10 ; []\OT1/cmr/m/n/10 )$
 []

[13]
Overfull \hbox (15.51614pt too wide) in paragraph at lines 1553--1567
\OT1/cmr/m/n/10 tion prob-lem [[],[]], as well as for mod-el-ing poly-mor-phism
 [[],[]],
 []

[14] [15] [16] [17]
Underfull \hbox (badness 10000) in paragraph at lines 2089--2093

 []

[18]
Underfull \hbox (badness 10000) in paragraph at lines 2103--2105

 []


Underfull \hbox (badness 10000) in paragraph at lines 2107--2110

 []


Underfull \hbox (badness 10000) in paragraph at lines 2111--2114

 []


Underfull \hbox (badness 10000) in paragraph at lines 2124--2126

 []


Underfull \hbox (badness 10000) in paragraph at lines 2136--2138

 []

[19]
Underfull \hbox (badness 10000) in paragraph at lines 2140--2143

 []


Underfull \hbox (badness 10000) in paragraph at lines 2167--2169

 []


Underfull \hbox (badness 10000) in paragraph at lines 2171--2189

 []

[20]
Underfull \hbox (badness 10000) in paragraph at lines 2202--2214

 []

Commutative Diagram: try the PostScript option for better results
[21] (rta03subJG.aux) ) 
Here is how much of TeX's memory you used:
 3241 strings out of 5913
 26669 string characters out of 48371
 96970 words of memory out of 200001
 6097 multiletter control sequences out of 10000
 11704 words of font info for 45 fonts, out of 80000 for 256
 15 hyphenation exceptions out of 2551
 110i,12n,22p,1022b,419s stack positions out of 600i,150n,200p,3000b,2000s

Output written on rta03subJG.dvi (21 pages, 115560 bytes).