This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) (format=pdflatex 2008.4.25)  17 DEC 2008 11:47
entering extended mode
 %&-line parsing enabled.
**fr
(./fr.tex
LaTeX2e <2005/12/01>
Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh
yphenation, loaded.
(/usr/share/texmf-texlive/tex/latex/base/report.cls
Document Class: report 2005/09/16 v1.4f Standard LaTeX document class
(/usr/share/texmf-texlive/tex/latex/base/size11.clo
File: size11.clo 2005/09/16 v1.4f Standard LaTeX file (size option)
)
\c@part=\count79
\c@chapter=\count80
\c@section=\count81
\c@subsection=\count82
\c@subsubsection=\count83
\c@paragraph=\count84
\c@subparagraph=\count85
\c@figure=\count86
\c@table=\count87
\abovecaptionskip=\skip41
\belowcaptionskip=\skip42
\bibindent=\dimen102
)
(/usr/share/texmf-texlive/tex/latex/ltxmisc/a4wide.sty
Package: a4wide 1994/08/30

(/usr/share/texmf-texlive/tex/latex/ntgclass/a4.sty
Package: a4 2004/04/15 v1.2g A4 based page layout
))
(/usr/share/texmf-texlive/tex/latex/amsfonts/amssymb.sty
Package: amssymb 2002/01/22 v2.2d

(/usr/share/texmf-texlive/tex/latex/amsfonts/amsfonts.sty
Package: amsfonts 2001/10/25 v2.2f
\@emptytoks=\toks14
\symAMSa=\mathgroup4
\symAMSb=\mathgroup5
LaTeX Font Info:    Overwriting math alphabet `\mathfrak' in version `bold'
(Font)                  U/euf/m/n --> U/euf/b/n on input line 132.
))
(/usr/share/texmf-texlive/tex/latex/base/inputenc.sty
Package: inputenc 2006/05/05 v1.1b Input encoding file
\inpenc@prehook=\toks15
\inpenc@posthook=\toks16

(/usr/share/texmf-texlive/tex/latex/base/latin1.def
File: latin1.def 2006/05/05 v1.1b Input encoding file
))
(/usr/share/texmf-texlive/tex/latex/base/makeidx.sty
Package: makeidx 2000/03/29 v1.0m Standard LaTeX package
)
\@indexfile=\write3
\openout3 = `fr.idx'.


Writing index file fr.idx
(/usr/share/texmf-texlive/tex/latex/graphics/color.sty
Package: color 2005/11/14 v1.0j Standard LaTeX Color (DPC)

(/etc/texmf/tex/latex/config/color.cfg
File: color.cfg 2007/01/18 v1.5 color configuration of teTeX/TeXLive
)
Package color Info: Driver file: pdftex.def on input line 130.

(/usr/share/texmf-texlive/tex/latex/pdftex-def/pdftex.def
File: pdftex.def 2007/01/08 v0.04d Graphics/color for pdfTeX
\Gread@gobject=\count88
))
(/usr/share/texmf-texlive/tex/latex/fancyvrb/fancyvrb.sty
Package: fancyvrb 1998/07/17

Style option: `fancyvrb' v2.6, with DG/SPQR fixes <1998/07/17> (tvz)
(/usr/share/texmf-texlive/tex/latex/graphics/keyval.sty
Package: keyval 1999/03/16 v1.13 key=value parser (DPC)
\KV@toks@=\toks17
)
\FV@CodeLineNo=\count89
\FV@InFile=\read1
\FV@TabBox=\box26
\c@FancyVerbLine=\count90
\FV@StepNumber=\count91
\FV@OutFile=\write4

No file fancyvrb.cfg.
) (/usr/share/texmf-texlive/tex/latex/pslatex/pslatex.sty
Package: pslatex 1996/07/24 v1.2 pslatex emulation (DPC)
LaTeX Font Info:    Redeclaring symbol font `operators' on input line 65.
LaTeX Font Info:    Overwriting symbol font `operators' in version `normal'
(Font)                  OT1/cmr/m/n --> OT1/ptmcm/m/n on input line 65.
LaTeX Font Info:    Overwriting symbol font `operators' in version `bold'
(Font)                  OT1/cmr/bx/n --> OT1/ptmcm/m/n on input line 65.
LaTeX Font Info:    Redeclaring symbol font `letters' on input line 66.
LaTeX Font Info:    Overwriting symbol font `letters' in version `normal'
(Font)                  OML/cmm/m/it --> OML/ptmcm/m/it on input line 66.
LaTeX Font Info:    Overwriting symbol font `letters' in version `bold'
(Font)                  OML/cmm/b/it --> OML/ptmcm/m/it on input line 66.
LaTeX Font Info:    Redeclaring symbol font `symbols' on input line 67.
LaTeX Font Info:    Overwriting symbol font `symbols' in version `normal'
(Font)                  OMS/cmsy/m/n --> OMS/pzccm/m/n on input line 67.
LaTeX Font Info:    Overwriting symbol font `symbols' in version `bold'
(Font)                  OMS/cmsy/b/n --> OMS/pzccm/m/n on input line 67.
LaTeX Font Info:    Redeclaring symbol font `largesymbols' on input line 68.
LaTeX Font Info:    Overwriting symbol font `largesymbols' in version `normal'
(Font)                  OMX/cmex/m/n --> OMX/psycm/m/n on input line 68.
LaTeX Font Info:    Overwriting symbol font `largesymbols' in version `bold'
(Font)                  OMX/cmex/m/n --> OMX/psycm/m/n on input line 68.
\symbold=\mathgroup6
\symitalic=\mathgroup7
LaTeX Font Info:    Redeclaring math alphabet \mathbf on input line 74.
LaTeX Font Info:    Overwriting math alphabet `\mathbf' in version `normal'
(Font)                  OT1/cmr/bx/n --> OT1/ptm/bx/n on input line 74.
LaTeX Font Info:    Overwriting math alphabet `\mathbf' in version `bold'
(Font)                  OT1/cmr/bx/n --> OT1/ptm/bx/n on input line 74.
LaTeX Font Info:    Redeclaring math alphabet \mathit on input line 75.
LaTeX Font Info:    Overwriting math alphabet `\mathit' in version `normal'
(Font)                  OT1/cmr/m/it --> OT1/ptm/m/it on input line 75.
LaTeX Font Info:    Overwriting math alphabet `\mathit' in version `bold'
(Font)                  OT1/cmr/bx/it --> OT1/ptm/m/it on input line 75.
)
(/usr/share/texmf-texlive/tex/latex/hyperref/hyperref.sty
Package: hyperref 2007/02/07 v6.75r Hypertext links for LaTeX
\@linkdim=\dimen103
\Hy@linkcounter=\count92
\Hy@pagecounter=\count93

(/usr/share/texmf-texlive/tex/latex/hyperref/pd1enc.def
File: pd1enc.def 2007/02/07 v6.75r Hyperref: PDFDocEncoding definition (HO)
)
(/etc/texmf/tex/latex/config/hyperref.cfg
File: hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive
)
(/usr/share/texmf-texlive/tex/latex/oberdiek/kvoptions.sty
Package: kvoptions 2006/08/22 v2.4 Connects package keyval with LaTeX options (
HO)
)
Package hyperref Info: Option `bookmarks' set `false' on input line 2238.
Package hyperref Info: Option `colorlinks' set `true' on input line 2238.
Package hyperref Info: Option `breaklinks' set `true' on input line 2238.
Package hyperref Info: Hyper figures OFF on input line 2288.
Package hyperref Info: Link nesting OFF on input line 2293.
Package hyperref Info: Hyper index ON on input line 2296.
Package hyperref Info: Plain pages OFF on input line 2303.
Package hyperref Info: Backreferencing ON on input line 2306.

Implicit mode ON; LaTeX internals redefined
Package hyperref Info: Bookmarks OFF on input line 2450.
(/usr/share/texmf-texlive/tex/latex/hyperref/backref.sty
Package: backref 2006/10/06 v1.27 Bibliographical back referencing
)
(/usr/share/texmf-texlive/tex/latex/ltxmisc/url.sty
\Urlmuskip=\muskip10
Package: url 2005/06/27  ver 3.2  Verb mode for urls, etc.
)
LaTeX Info: Redefining \url on input line 2599.
\Fld@menulength=\count94
\Field@Width=\dimen104
\Fld@charsize=\dimen105
\Choice@toks=\toks18
\Field@toks=\toks19
Package hyperref Info: Hyper figures OFF on input line 3102.
Package hyperref Info: Link nesting OFF on input line 3107.
Package hyperref Info: Hyper index ON on input line 3110.
Package hyperref Info: backreferencing ON on input line 3115.
Package hyperref Info: Link coloring ON on input line 3120.
\Hy@abspage=\count95
\c@Item=\count96
\c@Hfootnote=\count97
)
*hyperref using driver hpdftex*
(/usr/share/texmf-texlive/tex/latex/hyperref/hpdftex.def
File: hpdftex.def 2007/02/07 v6.75r Hyperref driver for pdfTeX
\Fld@listcount=\count98
)
\pagenrlog=\write5
\openout5 = `fr.pnr'.

 (./fr.aux)
\openout1 = `fr.aux'.

LaTeX Font Info:    Checking defaults for OML/cmm/m/it on input line 43.
LaTeX Font Info:    ... okay on input line 43.
LaTeX Font Info:    Checking defaults for T1/cmr/m/n on input line 43.
LaTeX Font Info:    ... okay on input line 43.
LaTeX Font Info:    Checking defaults for OT1/cmr/m/n on input line 43.
LaTeX Font Info:    ... okay on input line 43.
LaTeX Font Info:    Checking defaults for OMS/pzccm/m/n on input line 43.
LaTeX Font Info:    Try loading font information for OMS+pzccm on input line 43
.

(/usr/share/texmf-texlive/tex/latex/psnfss/omspzccm.fd
File: omspzccm.fd 2000/01/03 Fontinst v1.801 font definitions for OMS/pzccm.
)
LaTeX Font Info:    ... okay on input line 43.
LaTeX Font Info:    Checking defaults for OMX/cmex/m/n on input line 43.
LaTeX Font Info:    ... okay on input line 43.
LaTeX Font Info:    Checking defaults for U/cmr/m/n on input line 43.
LaTeX Font Info:    ... okay on input line 43.
LaTeX Font Info:    Checking defaults for PD1/pdf/m/n on input line 43.
LaTeX Font Info:    ... okay on input line 43.
Package hyperref Info: Link coloring ON on input line 43.

(/usr/share/texmf-texlive/tex/latex/hyperref/nameref.sty
Package: nameref 2006/12/27 v2.28 Cross-referencing by name of section

(/usr/share/texmf-texlive/tex/latex/oberdiek/refcount.sty
Package: refcount 2006/02/20 v3.0 Data extraction from references (HO)
)
\c@section@level=\count99
)
LaTeX Info: Redefining \ref on input line 43.
LaTeX Info: Redefining \pageref on input line 43.
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <24.88> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 47.
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <14.4> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 50.
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <12> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 54.
LaTeX Font Info:    Try loading font information for OT1+ptmcm on input line 58
.

(/usr/share/texmf-texlive/tex/latex/psnfss/ot1ptmcm.fd
File: ot1ptmcm.fd 2000/01/03 Fontinst v1.801 font definitions for OT1/ptmcm.
)
LaTeX Font Info:    Try loading font information for OML+ptmcm on input line 58
.

(/usr/share/texmf-texlive/tex/latex/psnfss/omlptmcm.fd
File: omlptmcm.fd 2000/01/03 Fontinst v1.801 font definitions for OML/ptmcm.
)
LaTeX Font Info:    Try loading font information for OMX+psycm on input line 58
.

(/usr/share/texmf-texlive/tex/latex/psnfss/omxpsycm.fd
File: omxpsycm.fd 2000/01/03 Fontinst v1.801 font definitions for OMX/psycm.
)
LaTeX Font Info:    Try loading font information for U+msa on input line 58.

(/usr/share/texmf-texlive/tex/latex/amsfonts/umsa.fd
File: umsa.fd 2002/01/19 v2.2g AMS font definitions
)
LaTeX Font Info:    Try loading font information for U+msb on input line 58.

(/usr/share/texmf-texlive/tex/latex/amsfonts/umsb.fd
File: umsb.fd 2002/01/19 v2.2g AMS font definitions
)
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <10.95> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 58.
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <8> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 58.
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <6> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 58.
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <10> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 64.

Underfull \hbox (badness 10000) in paragraph at lines 62--66

 []


Underfull \hbox (badness 3354) in paragraph at lines 67--70
\OT1/ptm/m/n/10.95 Mathematisches In-sti-tut, Bun-sen-stra^^Ye 3-5, D-
 []

[1

{/home/laurent/.texmf-var/fonts/map/pdftex/updmap/pdftex.map}]
LaTeX Font Info:    Font shape `OT1/phv/m/n' will be
(Font)              scaled to size 8.99994pt on input line 77.

Underfull \hbox (badness 10000) in paragraph at lines 83--85

 []

LaTeX Font Info:    Font shape `OMS/ptm/m/n' in size <10> not available
(Font)              Font shape `OMS/pzccm/m/n' tried instead on input line 87.

Underfull \hbox (badness 10000) in paragraph at lines 87--89

 []


Underfull \hbox (badness 10000) in paragraph at lines 91--94

 []


Underfull \hbox (badness 10000) in paragraph at lines 109--114

 []

[2] (./fr.toc [3

] [4] [5] [6] [7] [8])
\tf@toc=\write6
\openout6 = `fr.toc'.

 [9]
Chapter 1.
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <20.74> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 122.
[10

]
Chapter 2.
LaTeX Font Info:    Font shape `OT1/phv/m/n' will be
(Font)              scaled to size 9.85492pt on input line 147.
[11

] [12]
LaTeX Font Info:    Try loading font information for OML+pcr on input line 218.

 (/usr/share/texmf-texlive/tex/latex/psnfss/omlpcr.fd
File: omlpcr.fd 
)
LaTeX Font Info:    Font shape `OML/pcr/m/n' in size <10.95> not available
(Font)              Font shape `OML/cmm/m/it' tried instead on input line 218.
 [13] [14]
[15]
Chapter 3.

Underfull \hbox (badness 6792) in paragraph at lines 364--365
[]\OT1/ptm/m/n/10.95 More gen-eral ma-chines are ob-tained if one al-lows the s
tate-set $\OML/ptmcm/m/it/10.95 Q$ \OT1/ptm/m/n/10.95 to be a free
 []

[16

]
LaTeX Font Info:    Font shape `OT1/pcr/bx/n' in size <14.4> not available
(Font)              Font shape `OT1/pcr/b/n' tried instead on input line 399.
 [17] [18] [19] [20] [21] [22]
LaTeX Font Info:    Font shape `OT1/pcr/bx/n' in size <12> not available
(Font)              Font shape `OT1/pcr/b/n' tried instead on input line 850.
 [23] [24] [25] [26]
Underfull \hbox (badness 3449) in paragraph at lines 1142--1143
[]\OT1/ptm/m/n/10.95 If a ma-chine [] was cre-ated as a min-i-mized group/monoi
d/semigroup ma-chine, then
 []


Underfull \hbox (badness 10000) in paragraph at lines 1148--1152
[]\OT1/ptm/m/n/10.95 If [] was cre-ated us-ing \OT1/pcr/m/n/10.95 AsGroupFRMach
ine \OT1/ptm/m/n/10.95 ([][]3.3.4[][]), \OT1/pcr/m/n/10.95 AsMonoidFRMachine \O
T1/ptm/m/n/10.95 ([][]3.3.4[][]),
 []

[27]
Chapter 4.
[28

] [29]
Underfull \hbox (badness 1983) in paragraph at lines 1322--1324
[]\OT1/ptm/m/n/10.95 This func-tion con-structs a new FR el-e-ment. [] is a lis
t of FR el-e-ments, and [] is
 []


Underfull \hbox (badness 1831) in paragraph at lines 1322--1324
\OT1/ptm/m/n/10.95 a per-mu-ta-tion, trans-for-ma-tion or list. In that last ca
se, the re-sult-ing el-e-ment \OT1/pcr/m/n/10.95 g \OT1/ptm/m/n/10.95 sat-is-fi
es
 []

[30]
Underfull \hbox (badness 10000) in paragraph at lines 1389--1390
[]\OT1/ptm/m/n/10.95 In par-tic-u-lar, \OT1/pcr/m/n/10.95 DiagonalElement(0,e) 
\OT1/ptm/m/n/10.95 is the same as \OT1/pcr/m/n/10.95 VertexElement(1,e)\OT1/ptm
/m/n/10.95 ;
 []

[31] [32] [33] [34] [35] [36] [37] [38] [39]
Chapter 5.
[40

] [41] [42]
Underfull \hbox (badness 10000) in paragraph at lines 2221--2221
[][]\OT1/ptm/b/n/14.4 Operations and At-tributes for \OT1/pcr/b/n/14.4 MealyMac
hine\OT1/ptm/b/n/14.4 s and
 []


Underfull \hbox (badness 10000) in paragraph at lines 2229--2232

 []

[43] [44] [45] [46] [47] [48]
Overfull \hbox (55.59563pt too wide) in paragraph at lines 2663--2664
[]\OT1/ptm/m/n/10.95 The sec-ond com-mand is a short-hand for \OT1/pcr/m/n/10.9
5 VertexTransformationsFRMachine(UnderlyingFRMachine(e))\OT1/ptm/m/n/10.95 . 
 []

[49] [50] [51] [52] [53] [54] [55]
Chapter 6.

Underfull \hbox (badness 10000) in paragraph at lines 3147--3147
[][]\OT1/ptm/b/n/14.4 Methods and op-er-a-tions for \OT1/pcr/b/n/14.4 LinearFRM
achine\OT1/ptm/b/n/14.4 s and
 []

[56

] [57] [58]
Overfull \hbox (115.52515pt too wide) in paragraph at lines 3344--3345
[]\OT1/ptm/m/n/10.95 In par-tic-u-lar, \OT1/pcr/m/n/10.95 NestedMatrixState(e,[
],[])=e\OT1/ptm/m/n/10.95 , and \OT1/pcr/m/n/10.95 Activity(e,1)[i][j]=NestedMa
trixCoefficient(e,[i],[j])\OT1/ptm/m/n/10.95 ,
 []

[59] [60]
Underfull \hbox (badness 1122) in paragraph at lines 3522--3523
[]\OT1/ptm/m/n/10.95 Given a lin-ear el-e-ment [], this com-mand at-tempts to f
ind a de-com-po-si-tion of the form
 []


Underfull \hbox (badness 2781) in paragraph at lines 3522--3523
\OML/ptmcm/m/it/10.95 e \OT1/ptmcm/m/n/10.95 = \OML/ptmcm/m/it/10.95 LDU$\OT1/p
tm/m/n/10.95 , where $\OML/ptmcm/m/it/10.95 L$ \OT1/ptm/m/n/10.95 is lower tri-
an-gu-lar, $\OML/ptmcm/m/it/10.95 D$ \OT1/ptm/m/n/10.95 is di-ag-o-nal, and $\O
ML/ptmcm/m/it/10.95 U$ \OT1/ptm/m/n/10.95 is up-per tri-an-gu-lar (see
 []

[61]
Underfull \hbox (badness 1596) in paragraph at lines 3602--3604
[]\OT1/ptm/m/n/10.95 If [] is a Mealy ma-chine/element, the re-sult is a vec-to
r ma-chine/element. If [] is a
 []

[62] [63] [64]
Chapter 7.

Underfull \hbox (badness 1983) in paragraph at lines 3767--3770
[]\OT1/ptm/m/n/10.95 The max-i-mal length of words to con-sider in the search i
s con-trolled by the vari-able
 []

[65

] [66] [67] [68] [69] [70] [71]
Underfull \hbox (badness 10000) in paragraph at lines 4233--4235
[]\OT1/ptm/m/n/10.95 Furthermore, an op-tion "MealyEle-ment" can be passed to t
he func-tion, as
 []


Underfull \hbox (badness 3612) in paragraph at lines 4233--4235
\OT1/pcr/m/n/10.95 FRGroupByVirtualEndomorphism(f:MealyElement)\OT1/ptm/m/n/10.
95 , to re-quire the re-sult-ing group to be
 []

[72] [73] [74] [75] [76] [77] [78] [79]
Underfull \hbox (badness 4060) in paragraph at lines 4836--4837
[]\OT1/ptm/m/n/10.95 This func-tion re-turns \OT1/pcr/m/n/10.95 true \OT1/ptm/m
/n/10.95 if all el-e-ments of [] have the \OT1/ptm/m/it/10.95 open set con-di-t
ion\OT1/ptm/m/n/10.95 , see
 []

[80] [81] [82]
Underfull \hbox (badness 10000) in paragraph at lines 5094--5095
[]\OT1/ptm/m/n/10.95 This is the small-est group/monoid/semigroup \OT1/pcr/m/n/
10.95 P \OT1/ptm/m/n/10.95 such that []
 []


Underfull \hbox (badness 10000) in paragraph at lines 5094--5095
\OT1/ptm/m/n/10.95 is a sub-set of \OT1/pcr/m/n/10.95 FullSCGroup(AlphabetOfFRS
emigroup(g),P) \OT1/ptm/m/n/10.95 or
 []


Overfull \hbox (36.87662pt too wide) in paragraph at lines 5094--5095
\OT1/pcr/m/n/10.95 FullSCMonoid(AlphabetOfFRSemigroup(g),P) \OT1/ptm/m/n/10.95 
or \OT1/pcr/m/n/10.95 FullSCSemigroup(AlphabetOfFRSemigroup(g),P)\OT1/ptm/m/n/1
0.95 . 
 []

[83]
Underfull \hbox (badness 10000) in paragraph at lines 5201--5202
\OT1/ptm/m/n/10.95 ([][]10.1.2[][]), \OT1/pcr/m/n/10.95 GrigorchukGroup \OT1/pt
m/m/n/10.95 ([][]10.1.9[][]), \OT1/pcr/m/n/10.95 GrigorchukOverGroup \OT1/ptm/m
/n/10.95 ([][]10.1.10[][]), gen-er-al-ized
 []

[84] [85] [86] [87]
Chapter 8.

Underfull \hbox (badness 10000) in paragraph at lines 5441--5444
[]\OT1/ptm/m/n/10.95 Each [] is of the form \OT1/pcr/m/n/10.95 "name=[[...],...
,[...]]" \OT1/ptm/m/n/10.95 or of the form
 []


Underfull \hbox (badness 1629) in paragraph at lines 5441--5444
\OT1/pcr/m/n/10.95 "name=[[...],...,[...]]:out"\OT1/ptm/m/n/10.95 , namely a ma
-trix whose en-tries are al-ge-braic ex-pres-sions
 []


Overfull \hbox (88.59897pt too wide) in paragraph at lines 5445--5448
[]\OT1/ptm/m/n/10.95 The op-tion \OT1/pcr/m/n/10.95 IsVectorElement\OT1/ptm/m/n
/10.95 , passed e.g. as in \OT1/pcr/m/n/10.95 FRAlgebra(Rationals,"a=[[a,1],[a,
0]]":IsVectorElement)\OT1/ptm/m/n/10.95 ,
 []

[88

] [89] [90]
Chapter 9.
[91

] [92] [93] [94] [95] [96]
Chapter 10.

Underfull \hbox (badness 10000) in paragraph at lines 5985--6003

 []


Underfull \hbox (badness 2401) in paragraph at lines 6005--6008
[]\OT1/ptm/m/n/10.95 These are the fini-tary, bounded, polynomial-growth, finit
e-state, or un-re-stricted groups
 []


Underfull \hbox (badness 3930) in paragraph at lines 6005--6008
\OT1/ptm/m/n/10.95 act-ing on the bi-nary tree. They are re-spec-tively short-c
uts for \OT1/pcr/m/n/10.95 FullSCGroup([1..2])\OT1/ptm/m/n/10.95 ,
 []


Underfull \hbox (badness 10000) in paragraph at lines 6005--6008
\OT1/pcr/m/n/10.95 FullSCGroup([1..2],l)\OT1/ptm/m/n/10.95 , \OT1/pcr/m/n/10.95
 FullSCGroup([1..2],IsFinitaryFRSemigroup)\OT1/ptm/m/n/10.95 ,
 []


Overfull \hbox (62.05121pt too wide) in paragraph at lines 6005--6008
\OT1/pcr/m/n/10.95 FullSCGroup([1..2],IsBoundedFRSemigroup)\OT1/ptm/m/n/10.95 ,
 \OT1/pcr/m/n/10.95 FullSCGroup([1..2],IsPolynomialGrowthFRSemigroup)\OT1/ptm/m
/n/10.95 ,
 []

[97

]
Underfull \hbox (badness 10000) in paragraph at lines 6045--6046
[]\OT1/ptm/m/n/10.95 As par-tic-u-lar ex-am-ples, \OT1/pcr/m/n/10.95 BinaryKnea
dingMachine() \OT1/ptm/m/n/10.95 is the adding ma-chine;
 []


Underfull \hbox (badness 10000) in paragraph at lines 6045--6046
\OT1/pcr/m/n/10.95 BinaryKneadingGroup() \OT1/ptm/m/n/10.95 is the adding ma-ch
ine; and \OT1/pcr/m/n/10.95 BinaryKneadingGroup("1") \OT1/ptm/m/n/10.95 is
 []


Underfull \hbox (badness 10000) in paragraph at lines 6067--6070

 []


Underfull \hbox (badness 10000) in paragraph at lines 6091--6100

 []

[98]
Underfull \hbox (badness 10000) in paragraph at lines 6136--6145

 []


Underfull \hbox (badness 10000) in paragraph at lines 6147--6148
[]\OT1/ptm/m/n/10.95 These are re-spec-tively the same as \OT1/pcr/m/n/10.95 Ad
dingGroup(2)\OT1/ptm/m/n/10.95 , \OT1/pcr/m/n/10.95 AddingMachine(2) \OT1/ptm/m
/n/10.95 and
 []


Underfull \hbox (badness 1019) in paragraph at lines 6175--6177
[]\OT1/ptm/m/n/10.95 The first func-tion con-structs the group gen-er-ated by t
he mixer ma-chine. For ex-am-ples
 []

[99]
Underfull \hbox (badness 10000) in paragraph at lines 6233--6234
[]\OT1/ptm/m/n/10.95 These groups are \OT1/pcr/m/n/10.95 MixerGroup \OT1/ptm/m/
n/10.95 ([][]10.1.6[][])s. The most fa-mous ex-am-ple is
 []


Underfull \hbox (badness 7869) in paragraph at lines 6235--6236
[]\OT1/ptm/m/n/10.95 These groups are all 4-generated and in-fi-nite. They are 
de-scribed in [[]][].
 []


Underfull \hbox (badness 1484) in paragraph at lines 6235--6236
\OT1/pcr/m/n/10.95 GrigorchukGroups([1]) \OT1/ptm/m/n/10.95 is in-fi-nite di-he
-dral. If [] con-tains at least 2 dif-fer-ent dig-
 []

[100]
Underfull \hbox (badness 10000) in paragraph at lines 6260--6266

 []


Underfull \hbox (badness 4378) in paragraph at lines 6268--6270
[]\OT1/ptm/m/n/10.95 This is Grig-orchuk's first group, in-tro-duced in [[]][].
 It is a 4-generated in-fi-
 []


Underfull \hbox (badness 2894) in paragraph at lines 6268--6270
\OT1/ptm/m/n/10.95 nite tor-sion group, and has in-ter-me-di-ate word growth. I
t could have been de-fined as
 []


Underfull \hbox (badness 10000) in paragraph at lines 6271--6273
[]\OT1/ptm/m/n/10.95 The com-mand \OT1/pcr/m/n/10.95 EpimorphismFromFpGroup(Gri
gorchukGroup,n) \OT1/ptm/m/n/10.95 will will con-
 []


Underfull \hbox (badness 5667) in paragraph at lines 6271--6273
\OT1/ptm/m/n/10.95 struct an ap-prox-i-mat-ing pre-sen-ta-tion for the Grig-orc
huk group, as proven in [[]][].
 []


Underfull \hbox (badness 7308) in paragraph at lines 6271--6273
\OT1/ptm/m/n/10.95 Adding the re-la-tions \OT1/pcr/m/n/10.95 Image(sigma^(n-2),
(a*d)^2)\OT1/ptm/m/n/10.95 , \OT1/pcr/m/n/10.95 Image(sigma^(n-1),(a*b)^2) \OT1
/ptm/m/n/10.95 and
 []


Underfull \hbox (badness 10000) in paragraph at lines 6279--6282

 []


Underfull \hbox (badness 10000) in paragraph at lines 6303--6306

 []


Underfull \hbox (badness 10000) in paragraph at lines 6308--6309
[]\OT1/ptm/m/n/10.95 This is a group with same clo-sure as the Grig-orchuk grou
p (see
 []


Underfull \hbox (badness 3492) in paragraph at lines 6308--6309
\OT1/pcr/m/n/10.95 GrigorchukGroup \OT1/ptm/m/n/10.95 ([][]10.1.9[][])), but no
t iso-mor-phic to it. It could have been de-fined as
 []

[101]
Underfull \hbox (badness 10000) in paragraph at lines 6324--6330

 []


Underfull \hbox (badness 10000) in paragraph at lines 6364--6365
[]\OT1/ptm/m/n/10.95 If \OT1/pcr/m/n/10.95 l=[(1,2),(1,2),()]\OT1/ptm/m/n/10.95
 , this is \OT1/pcr/m/n/10.95 AleshinGroup \OT1/ptm/m/n/10.95 ([][]10.1.14[][])
. More gen-er-ally, if
 []


Underfull \hbox (badness 1320) in paragraph at lines 6364--6365
\OT1/pcr/m/n/10.95 l=[(1,2,(1,2),(),...,()] \OT1/ptm/m/n/10.95 has odd length, 
this is a free group of rank \OT1/pcr/m/n/10.95 Length(l)\OT1/ptm/m/n/10.95 , s
ee
 []


Underfull \hbox (badness 10000) in paragraph at lines 6375--6381

 []


Underfull \hbox (badness 10000) in paragraph at lines 6383--6385
[]\OT1/ptm/m/n/10.95 This is the first ex-am-ple of non-abelian free group. It 
is the group gen-er-
 []


Underfull \hbox (badness 10000) in paragraph at lines 6383--6385
\OT1/ptm/m/n/10.95 ated by \OT1/pcr/m/n/10.95 AleshinMachine([(1,2),(1,2),()])\
OT1/ptm/m/n/10.95 . It could have been de-fined as
 []


Underfull \hbox (badness 10000) in paragraph at lines 6383--6385
\OT1/pcr/m/n/10.95 FRGroup("a=\OML/cmm/m/it/10.95 <\OT1/pcr/m/n/10.95 b,c\OML/c
mm/m/it/10.95 >\OT1/pcr/m/n/10.95 (1,2)","b=\OML/cmm/m/it/10.95 <\OT1/pcr/m/n/1
0.95 c,b\OML/cmm/m/it/10.95 >\OT1/pcr/m/n/10.95 (1,2)","c=\OML/cmm/m/it/10.95 <
\OT1/pcr/m/n/10.95 a,a\OML/cmm/m/it/10.95 >\OT1/pcr/m/n/10.95 ")\OT1/ptm/m/n/10
.95 , but is rather de-fined us-ing
 []

[102]
Underfull \hbox (badness 10000) in paragraph at lines 6391--6397

 []


Underfull \hbox (badness 10000) in paragraph at lines 6419--6422

 []


Underfull \hbox (badness 10000) in paragraph at lines 6460--6466

 []

[103]
Underfull \hbox (badness 4647) in paragraph at lines 6468--6470
[]\OT1/ptm/m/n/10.95 This is an in-fi-nite, 2-generated, tor-sion 3-group. It c
ould have been de-fined as
 []


Underfull \hbox (badness 1264) in paragraph at lines 6490--6491
\OT1/ptm/m/n/10.95 of non-uniform ex-po-nen-tial growth (see [[]][]), and \OT1/
pcr/m/n/10.95 NeumannGroup(Group((1,2,3))) \OT1/ptm/m/n/10.95 is
 []


Underfull \hbox (badness 10000) in paragraph at lines 6499--6505

 []


Underfull \hbox (badness 10000) in paragraph at lines 6519--6522

 []

[104]
Underfull \hbox (badness 10000) in paragraph at lines 6574--6577

 []


Underfull \hbox (badness 10000) in paragraph at lines 6584--6585
[]\OT1/ptm/m/n/10.95 It ad-mits an en-do-mor-phism on its de-rived sub-group. I
n-deed
 []


Underfull \hbox (badness 10000) in paragraph at lines 6584--6585
\OT1/pcr/m/n/10.95 FRElement(1,Comm(a,b))=Comm(c^-1,b/a)\OT1/ptm/m/n/10.95 , \O
T1/pcr/m/n/10.95 FRElement(1,Comm(a,c))=Comm(a/b,c)\OT1/ptm/m/n/10.95 ,
 []


Underfull \hbox (badness 10000) in paragraph at lines 6591--6594

 []


Underfull \hbox (badness 2894) in paragraph at lines 6596--6598
[]\OT1/ptm/m/n/10.95 This group was stud-ied in [[]][]. It is frac-tal, but not
 con-tract-ing. It could
 []


Underfull \hbox (badness 10000) in paragraph at lines 6596--6598
\OT1/ptm/m/n/10.95 have been de-fined as \OT1/pcr/m/n/10.95 FRGroup("a=\OML/cmm
/m/it/10.95 <\OT1/pcr/m/n/10.95 ,b\OML/cmm/m/it/10.95 >\OT1/pcr/m/n/10.95 (1,2)
","b=\OML/cmm/m/it/10.95 <\OT1/pcr/m/n/10.95 a,c\OML/cmm/m/it/10.95 >\OT1/pcr/m
/n/10.95 ","c=\OML/cmm/m/it/10.95 <\OT1/pcr/m/n/10.95 a,a^-1\OML/cmm/m/it/10.95
 >\OT1/pcr/m/n/10.95 (1,2)")]]\OML/cmm/m/it/10.95 >\OT1/ptm/m/n/10.95 ,
 []


Underfull \hbox (badness 8075) in paragraph at lines 6596--6598
\OT1/ptm/m/n/10.95 but is rather de-fined us-ing Mealy el-e-ments. It par-tiall
y ad-mits branch-ing on its
 []


Underfull \hbox (badness 10000) in paragraph at lines 6596--6598
\OT1/ptm/m/n/10.95 sub-group \OT1/pcr/m/n/10.95 Subgroup(G,[a^2,(a^2)^b,(a^2)^c
])\OT1/ptm/m/n/10.95 , and, set-ting \OT1/pcr/m/n/10.95 x=Comm(a^2,b)\OT1/ptm/m
/n/10.95 , on
 []


Underfull \hbox (badness 10000) in paragraph at lines 6604--6607

 []

[105] [106] [107]
Underfull \hbox (badness 10000) in paragraph at lines 6744--6750

 []


Underfull \hbox (badness 10000) in paragraph at lines 6762--6768

 []


Underfull \hbox (badness 10000) in paragraph at lines 6786--6789

 []


Underfull \hbox (badness 10000) in paragraph at lines 6811--6814

 []

[108]
Underfull \hbox (badness 10000) in paragraph at lines 6827--6830

 []


Underfull \hbox (badness 10000) in paragraph at lines 6843--6846

 []

[109] [110] [111] [112] [113] [114]
Chapter 11.

Underfull \hbox (badness 10000) in paragraph at lines 7204--7207

 []

[115

]
Underfull \hbox (badness 10000) in paragraph at lines 7220--7223

 []

[116] [117] [118] [119] [120] [121] [122]
Chapter 12.

Underfull \hbox (badness 10000) in paragraph at lines 7782--7785

 []


Underfull \hbox (badness 10000) in paragraph at lines 7795--7798

 []


Underfull \hbox (badness 10000) in paragraph at lines 7807--7810

 []


Underfull \hbox (badness 10000) in paragraph at lines 7819--7822

 []


Underfull \hbox (badness 10000) in paragraph at lines 7831--7834

 []


Underfull \hbox (badness 10000) in paragraph at lines 7843--7864

 []

[123

]
Underfull \hbox (badness 10000) in paragraph at lines 7878--7879
[]\OT1/ptm/m/n/10.95 The fourth and fifth com-mand com-press the newly cre-ated
 pe-ri-odic list, see
 []


Underfull \hbox (badness 10000) in paragraph at lines 7905--7908

 []

[124] [125]
LaTeX Font Info:    Font shape `OT1/pcr/bx/n' in size <10.95> not available
(Font)              Font shape `OT1/pcr/b/n' tried instead on input line 8020.

Underfull \hbox (badness 2762) in paragraph at lines 8042--8043
\OT1/ptm/m/n/10.95 If the first ar-gu-ment is an in-te-ger \OT1/pcr/m/n/10.95 n
 \OT1/ptm/m/n/10.95 and not a record, the com-mand is in-ter-preted as
 []


Underfull \hbox (badness 10000) in paragraph at lines 8044--8045
[]\OT1/pcr/m/n/10.95 WordGrowth(...,rec(draw:=true)) \OT1/ptm/m/n/10.95 may be 
ab-bre-vi-ated as \OT1/pcr/m/n/10.95 Draw(...)\OT1/ptm/m/n/10.95 ;
 []


Underfull \hbox (badness 10000) in paragraph at lines 8044--8045
\OT1/pcr/m/n/10.95 WordGrowth(...,rec(ball:=n)) \OT1/ptm/m/n/10.95 may be ab-br
e-vi-ated as \OT1/pcr/m/n/10.95 Ball(...,n)\OT1/ptm/m/n/10.95 ;
 []

[126] [127] [128]
Underfull \hbox (badness 10000) in paragraph at lines 8281--8282
[]\OT1/ptm/m/n/10.95 This func-tion con-structs an en-do-mor-phism of the group
,monoid or semi-
 []


Underfull \hbox (badness 10000) in paragraph at lines 8281--8282
\OT1/ptm/m/n/10.95 group [] spec-i-fied by send-ing gen-er-a-tor num-ber $\OML/
ptmcm/m/it/10.95 i$ \OT1/ptm/m/n/10.95 to the $\OML/ptmcm/m/it/10.95 i$\OT1/ptm
/m/n/10.95 th en-try in
 []


Underfull \hbox (badness 10000) in paragraph at lines 8281--8282
[]\OT1/ptm/m/n/10.95 . It is a short-cut for a call to \OT1/pcr/m/n/10.95 Group
HomomorphismByImagesNC \OT1/ptm/m/n/10.95 or
 []


Underfull \hbox (badness 10000) in paragraph at lines 8296--8297
[]\OT1/ptm/m/n/10.95 This func-tion con-structs a ho-mo-mor-phism of the group,
monoid or semi-
 []


Underfull \hbox (badness 10000) in paragraph at lines 8296--8297
\OT1/ptm/m/n/10.95 group [] spec-i-fied by send-ing gen-er-a-tor num-ber $\OML/
ptmcm/m/it/10.95 i$ \OT1/ptm/m/n/10.95 to the $\OML/ptmcm/m/it/10.95 i$\OT1/ptm
/m/n/10.95 th en-try in
 []


Underfull \hbox (badness 10000) in paragraph at lines 8296--8297
[]\OT1/ptm/m/n/10.95 . It is a short-cut for a call to \OT1/pcr/m/n/10.95 Group
HomomorphismByImagesNC \OT1/ptm/m/n/10.95 or
 []

[129]
Underfull \hbox (badness 10000) in paragraph at lines 8303--8312

 []

[130]
Underfull \hbox (badness 10000) in paragraph at lines 8392--8395

 []


Underfull \hbox (badness 10000) in paragraph at lines 8434--8437

 []

[131]
Underfull \hbox (badness 10000) in paragraph at lines 8455--8458

 []

(./fr.bbl (./fr.brf)
\tf@brf=\write7
\openout7 = `fr.brf'.

 [132]
Underfull \hbox (badness 5161) in paragraph at lines 12--12
[]\OT1/ptm/m/n/10.95 R. Bacher.  De-ter-mi-nants re-lated to bi-no-mial co-ef-f
i-cients mod-ulo $\OT1/ptmcm/m/n/10.95 2$ \OT1/ptm/m/n/10.95 and $\OT1/ptmcm/m/
n/10.95 4$\OT1/ptm/m/n/10.95 .
 []


Underfull \hbox (badness 10000) in paragraph at lines 73--73
[]\OT1/ptm/m/n/10.95 L. Bartholdi and I. I. Reznykov.  A mealy ma-chine of grow
th $\OML/ptmcm/m/it/10.95 n[]$\OT1/ptm/m/n/10.95 .
 []

[133

] [134] [135]) (./fr.ind [136] [137

] [138] [139] [140] [141]) (./fr.aux) ) 
Here is how much of TeX's memory you used:
 4951 strings out of 95086
 72076 string characters out of 1183255
 132235 words of memory out of 1500000
 7267 multiletter control sequences out of 10000+50000
 49843 words of font info for 101 fonts, out of 1200000 for 2000
 28 hyphenation exceptions out of 8191
 25i,7n,29p,673b,625s stack positions out of 5000i,500n,6000p,200000b,5000s
{/usr/share/texmf-texlive/fonts/enc/dvip
s/base/8r.enc}</usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmex10.pfb></usr
/share/texmf-texlive/fonts/type1/bluesky/cm/cmmi10.pfb></usr/share/texmf-texliv
e/fonts/type1/bluesky/cm/cmr10.pfb></usr/share/texmf-texlive/fonts/type1/bluesk
y/cm/cmsy10.pfb></usr/share/texmf-texlive/fonts/type1/public/cmex/fmex9.pfb></u
sr/share/texmf-texlive/fonts/type1/bluesky/ams/msam10.pfb></usr/share/texmf-tex
live/fonts/type1/bluesky/ams/msbm10.pfb></usr/share/texmf-texlive/fonts/type1/u
rw/courier/ucrb8a.pfb></usr/share/texmf-texlive/fonts/type1/urw/courier/ucrr8a.
pfb></usr/share/texmf-texlive/fonts/type1/urw/courier/ucrro8a.pfb></usr/share/t
exmf-texlive/fonts/type1/urw/helvetic/uhvr8a.pfb></usr/share/texmf-texlive/font
s/type1/urw/symbol/usyr.pfb></usr/share/texmf-texlive/fonts/type1/urw/times/utm
b8a.pfb></usr/share/texmf-texlive/fonts/type1/urw/times/utmr8a.pfb></usr/share/
texmf-texlive/fonts/type1/urw/times/utmr8a.pfb></usr/share/texmf-texlive/fonts/
type1/urw/times/utmri8a.pfb>
Output written on fr.pdf (141 pages, 796714 bytes).
PDF statistics:
 2440 PDF objects out of 2487 (max. 8388607)
 773 named destinations out of 1000 (max. 131072)
 17 words of extra memory for PDF output out of 10000 (max. 10000000)

