% LLNCS DOCUMENT STYLE -- version 1.2
% for LaTeX version 2.09

% This style file is an adaptation of
% the original LaTeX article.sty

\typeout{Document Style `llncs', <version 1.2>}

\frenchspacing
\def~{\penalty\@M\kern3pt}

% Language dependant section
\def\literaturename{References}
\def\contentsname{Table of Contents}
\def\listoffiguresname{List of Figures}
\def\figurename{Fig.\thinspace}
\def\listoftablesname{List of Tables}
\def\tablename{Table }
\def\abstractname{Abstract.}
\newif\if@deutsch\@deutschfalse
%
\def\ds@deutsch{\typeout{German version}
\def\literaturename{Literatur}
\def\contentsname{Inhaltsverzeichnis}
\def\listoffiguresname{Abbildungsverzeichnis}
\def\figurename{Abb.\thinspace}
\def\listoftablesname{Tabellenverzeichnis}
\def\tablename{Tabelle }
\def\abstractname{Zusammenfassung.}
\@deutschtrue}

\def\thebibliography#1{\section*{\literaturename}\small\list
  {\arabic{enumi}.}{\settowidth\labelwidth{#1.}\leftmargin\labelwidth
    \advance\leftmargin\labelsep
    \usecounter{enumi}}
    \def\newblock{\hskip .11em plus .33em minus -.07em}
    \sloppy
    \sfcode`\.=1000\relax}

\def\ds@citeauthoryear{\def\thebibliography##1{\section*{\literaturename}%
    \small\list{}{\settowidth\labelwidth{}\leftmargin\parindent
    \itemindent=-\parindent
    \labelsep=\z@
    \usecounter{enumi}}%
    \def\newblock{\hskip .11em plus .33em minus -.07em}%
    \sloppy
    \sfcode`\.=1000\relax}%
    \def\@cite##1{##1}%
    \def\@lbibitem[##1]##2{\item[]\if@filesw
      {\def\protect####1{\string ####1\space}\immediate
    \write\@auxout{\string\bibcite{##2}{##1}}}\fi\ignorespaces}}%

\newif\if@envcountreset\@envcountresetfalse
\def\ds@envcountreset{\@envcountresettrue}

\def\@mbi{cmmib10}
\def\@ptsize{0} \@namedef{ds@11pt}{\def\@ptsize{1}}
\@namedef{ds@12pt}{\def\@ptsize{2}}
\def\ds@twoside{\@twosidetrue \@mparswitchtrue}
\def\ds@draft{\overfullrule
5pt}
\@options

\ds@twoside

\lineskip 1pt \normallineskip 1pt
\def\baselinestretch{1}

\def\@normalsize{\@setsize\normalsize{12pt}\xpt\@xpt
\abovedisplayskip=3 mm plus6pt minus 4pt
\belowdisplayskip=3 mm plus6pt minus 4pt
\abovedisplayshortskip=0mm plus6pt minus 2pt
\belowdisplayshortskip=2 mm plus4pt minus 4pt}

\mathchardef\Gamma="0100
\mathchardef\Delta="0101
\mathchardef\Theta="0102
\mathchardef\Lambda="0103
\mathchardef\Xi="0104
\mathchardef\Pi="0105
\mathchardef\Sigma="0106
\mathchardef\Upsilon="0107
\mathchardef\Phi="0108
\mathchardef\Psi="0109
\mathchardef\Omega="010A

\def\small{\@setsize\small{11pt}\ixpt\@ixpt
\abovedisplayskip=2.5 mm plus5pt minus 3pt
\belowdisplayskip=2.5 mm plus5pt minus 3pt
\abovedisplayshortskip=0mm plus6pt minus 2pt
\belowdisplayshortskip=2 mm plus4pt minus 4pt
\def\@listi{\leftmargin\leftmargini\topsep 4pt plus 2pt minus 2pt}}

\def\footnotesize{\@setsize\footnotesize{11pt}\ixpt\@ixpt
\abovedisplayskip=2.5 mm plus5pt minus 3pt
\belowdisplayskip=2.5 mm plus5pt minus 3pt
\abovedisplayshortskip=0mm plus6pt minus 2pt
\belowdisplayshortskip=2 mm plus4pt minus 4pt
\def\@listi{\leftmargin\leftmargini\topsep 4pt plus 2pt minus 2pt}}

\def\scriptsize{\@setsize\scriptsize{8.4pt}\viipt\@viipt}

\def\tiny{\@setsize\tiny{6pt}\vpt\@vpt}
\def\large{\@setsize\large{13.2pt}\xipt\@xipt}
\def\Large{\@setsize\Large{14.4pt}\xiipt\@xiipt}
\def\LARGE{\@setsize\LARGE{16.8pt}\xivpt\@xivpt}
\def\huge{\@setsize\huge{22pt}\xxpt\@xxpt}
\def\Huge{\@setsize\Huge{30pt}\xxvpt\@xxvpt}
\@normalsize

\if@twoside
   \oddsidemargin  44pt
   \evensidemargin 82pt
   \marginparwidth 107pt
\else \oddsidemargin 63pt \evensidemargin 63pt
 \marginparwidth 90pt
\fi
\marginparsep 11pt
\topmargin 11pt \headheight 12pt \headsep 13.66pt
\footheight 12pt \footskip 30pt
\textwidth 12.2truecm
\textheight 19.3truecm
\columnsep 1cc \columnseprule 0pt

\footnotesep 7.7pt
\skip\footins 9pt plus 4pt minus 2pt
\floatsep 12pt plus 2pt minus 2pt
\textfloatsep 8mm plus 2pt minus 4pt
\intextsep 8mm plus 2pt minus 2pt
\@maxsep 8mm

\dblfloatsep 12pt plus 2pt minus 2pt
\dbltextfloatsep 20pt plus 2pt minus 4pt
\@dblmaxsep 20pt

\@fptop 0pt plus 1fil \@fpsep 8pt plus 2fil \@fpbot 0pt plus 1fil
\@dblfptop0pt plus1fil \@dblfpsep8pt plus2fil\@dblfpbot 0pt plus1fil
\marginparpush 5pt

\parskip 0pt plus 1pt \parindent 1.5em \topsep 8pt plus 2pt minus 4pt
\partopsep 2pt plus 1pt minus 1pt \itemsep \z@
\@lowpenalty 51 \@medpenalty 151 \@highpenalty 301
\@beginparpenalty-\@lowpenalty\@endparpenalty -\@lowpenalty\@itempenalty
-\@lowpenalty

\def\vec#1{\mathchoice{\mbox{\boldmath$\displaystyle\bf#1$}}
{\mbox{\boldmath$\textstyle\bf#1$}}
{\mbox{\boldmath$\scriptstyle\bf#1$}}
{\mbox{\boldmath$\scriptscriptstyle\bf#1$}}}

\def\@sect#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth
  \def\@svsec{}\else
  \refstepcounter{#1}\edef\@svsec{\csname the#1\endcsname\quad }\fi
  \@tempskipa #5\relax
   \ifdim \@tempskipa>\z@
  \begingroup #6\relax
  \noindent{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par}
  \endgroup
    \csname #1mark\endcsname{#7}\addcontentsline
   {toc}{#1}{\ifnum #2>\c@secnumdepth \else
            \protect\numberline{\csname the#1\endcsname}\fi
          #7}\else
  \def\@svsechd{#6\hskip #3\@svsec #8\csname #1mark\endcsname
            {#7}\addcontentsline
             {toc}{#1}{\ifnum #2>\c@secnumdepth \else
               \protect\numberline{\csname the#1\endcsname}\fi
             #7}}\fi
  \@xsect{#5}}

\def\part{\par \addvspace{4ex} \@afterindentfalse \secdef\@part\@spart}

\def\@part[#1]#2{\ifnum \c@secnumdepth >\m@ne \refstepcounter{part}
\addcontentsline{toc}{part}{\thepart \hspace{1em}#1}\else
\addcontentsline{toc}{part}{#1}\fi { \parindent 0pt \raggedright
 \ifnum \c@secnumdepth >\m@ne \Large \bf
 Part\thepart\par\nobreak\fi\huge
\bf #2\markboth{}{}\par } \nobreak \vskip 3ex \@afterheading }

\def\@spart#1{{\parindent 0pt \raggedright
 \huge \bf
 #1\par} \nobreak \vskip 3ex \@afterheading }

\def\section{\@startsection {section}{1}{\z@}{-18pt plus -4pt minus
-4pt}{12pt plus 4pt minus 4pt}{\Large\bf\boldmath
\pretolerance=10000\relax\rightskip=0pt plus8em}}
\def\subsection{\@startsection{subsection}{2}{\z@}{-18pt plus-4pt minus
 -4pt}{8pt plus 4pt minus 4pt}{\normalsize\bf\boldmath
\pretolerance=10000\relax\rightskip=0pt plus8em}}
\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-18pt plus-4pt
 minus -4pt}{-0.5em plus -.22em minus -0.1em}{\normalsize\bf\boldmath}}
\def\paragraph{\@startsection{paragraph}{4}{\z@}{-12pt plus -4pt minus
 -4pt}{-0.5em plus -.22em minus -0.1em}{\normalsize\it}}
\def\subparagraph#1{\typeout{LLNCS Warning: You should not use
\protect\subparagraph \space in this style.}\vskip0.5cm
You should not use $\backslash${\tt subparagraph} in this
style.\vskip0.5cm}

\setcounter{secnumdepth}{2}

\def\appendix{\par
 \setcounter{section}{0}
 \setcounter{subsection}{0}
 \def\thesection{\Alph{section}}}

\leftmargini 17pt     \leftmarginii 17pt
\leftmarginiii 17pt   \leftmarginiv 17pt
\leftmarginv 10pt       \leftmarginvi 10pt
\leftmargin\leftmargini \labelwidth\leftmargini
\advance\labelwidth-\labelsep
\labelsep 5pt
\parsep 0pt plus 1pt
\def\@listi{\leftmargin\leftmargini}
\def\@listii{\leftmargin\leftmarginii
 \labelwidth\leftmarginii\advance\labelwidth-\labelsep
 \topsep 0pt plus 1pt}
\def\@listiii{\leftmargin\leftmarginiii
 \labelwidth\leftmarginiii\advance\labelwidth-\labelsep
 \topsep 0pt plus 1pt}
\def\@listiv{\leftmargin\leftmarginiv
 \labelwidth\leftmarginiv\advance\labelwidth-\labelsep
 \topsep 0pt plus 1pt}
\def\@listv{\leftmargin\leftmarginv
 \labelwidth\leftmarginv\advance\labelwidth-\labelsep
 \topsep 0pt plus 1pt}
\def\@listvi{\leftmargin\leftmarginvi
 \labelwidth\leftmarginvi\advance\labelwidth-\labelsep
 \topsep 0pt plus 1pt}

\def\labelenumi{\arabic{enumi}.}
\def\theenumi{\arabic{enumi}}
\def\labelenumii{(\alph{enumii})}
\def\theenumii{\alph{enumii}}
\def\p@enumii{\theenumi}
\def\labelenumiii{\roman{enumiii}.}
\def\theenumiii{\roman{enumiii}}
\def\p@enumiii{\theenumi(\theenumii)}
\def\labelenumiv{\Alph{enumiv}.}
\def\theenumiv{\Alph{enumiv}}
\def\p@enumiv{\p@enumiii\theenumiii}

\def\labelitemi{\bf --}
\def\labelitemii{$\bullet$}
\def\labelitemiii{$\ast$}
\def\labelitemiv{$\cdot$}

\def\verse{\let\\=\@centercr
 \list{}{\itemsep\z@ \itemindent -1.5em\listparindent \itemindent
 \rightmargin\leftmargin\advance\leftmargin 1.5em}\item[]}
\let\endverse\endlist
\def\quotation{\list{}{\listparindent 1.5em
 \itemindent\listparindent
 \rightmargin\leftmargin}\item[]}
\let\endquotation=\endlist
\def\quote{\list{}{\rightmargin\leftmargin}\item[]}
\let\endquote=\endlist

\def\descriptionlabel#1{\hspace\labelsep \bf #1}
\def\description{\list{}{\labelwidth\z@ \itemindent-\leftmargin
 \let\makelabel\descriptionlabel}}
\let\enddescription\endlist

\def\theequation{\arabic{equation}}

\def\titlepage{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn
 \else \newpage \fi \thispagestyle{empty}\c@page\z@}
\def\endtitlepage{\if@restonecol\twocolumn \else \newpage \fi}

\arraycolsep 1.4pt \tabcolsep 1.4pt \arrayrulewidth .4pt \doublerulesep
2pt
\tabbingsep \labelsep

\skip\@mpfootins = \skip\footins
\fboxsep = 3pt \fboxrule = .4pt

\newcounter{part}
\newcounter {section}
\newcounter {subsection}[section]
\newcounter {subsubsection}[subsection]
\newcounter {paragraph}[subsubsection]

\def\thepart{\Roman{part}}
\def\thesection {\arabic{section}}
\def\thesubsection {\thesection.\arabic{subsection}}
\def\thesubsubsection {\thesubsection.\arabic{subsubsection}}
\def\theparagraph {\thesubsubsection.\arabic{paragraph}}

\def\@pnumwidth{1.55em}
\def\@tocrmarg {2.55em}
\def\@dotsep{4.5}
\setcounter{tocdepth}{3}

\def\tableofcontents{\section*{\contentsname}
 \@starttoc{toc}}
\def\l@part#1#2{\addpenalty{\@secpenalty}
 \addvspace{2.25em plus 1pt} \begingroup
 \@tempdima 3em \parindent \z@ \rightskip \@pnumwidth \parfillskip
-\@pnumwidth
 {\Large \bf \leavevmode #1\hfil \hbox to\@pnumwidth{\hss #2}}\par
 \nobreak \endgroup}
%
\def\numberline#1{\advance\hangindent by\@tempdima%
\hbox to\@tempdima{\hss#1\enspace}}
%
\def\bf@dottedtocline#1#2#3#4#5{\ifnum #1>\c@tocdepth \else
  \vskip \z@ plus .2pt
  {\leftskip #2\relax \rightskip \@tocrmarg \parfillskip -\rightskip
    \parindent #2\relax\@afterindenttrue
   \interlinepenalty\@M
   \leavevmode
   \@tempdima #3\relax \advance\leftskip \@tempdima \hbox{}\hskip
   -\leftskip
{\bf#4}\nobreak\leaders\hbox{$\m@th \mkern \@dotsep mu.\mkern \@dotsep
       mu$}\hfill \nobreak \hbox to\@pnumwidth{\hfil\rm #5}\par}\fi}
%
\def\l@section{\vskip2mm\bf@dottedtocline{1}{0em}{1.7em}}
\def\l@subsection{\@dottedtocline{2}{1.7em}{2.3em}}
\def\l@subsubsection{\@dottedtocline{3}{4em}{2em}}
\def\l@paragraph{\@dottedtocline{4}{6em}{2em}}
\def\l@subparagraph{\@dottedtocline{5}{8em}{2em}}
\def\listoffigures{\section*{\listoffiguresname\markboth
 {\listoffiguresname}{\listoffiguresname}}\@starttoc{lof}}
\def\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}
\def\listoftables{\section*{\listoftablesname\markboth
 {\listoftablesname}{\listoftablesname}}\@starttoc{lot}}
\let\l@table\l@figure

\def\endthebibliography{\endlist\normalsize}

\newif\if@restonecol
\def\theindex{\@restonecoltrue\if@twocolumn\@restonecolfalse\fi
\columnseprule \z@
\columnsep 35pt\twocolumn[\section*{Index}]
 \markboth{Index}{Index}\thispagestyle{plain}\parindent\z@
 \parskip\z@ plus .3pt\relax\let\item\@idxitem}
\def\@idxitem{\par\hangindent 40pt}
\def\subitem{\par\hangindent 40pt \hspace*{20pt}}
\def\subsubitem{\par\hangindent 40pt \hspace*{30pt}}
\def\endtheindex{\if@restonecol\onecolumn\else\clearpage\fi}
\def\indexspace{\par \vskip 10pt plus 5pt minus 3pt\relax}

\def\footnoterule{\kern-3\p@\hrule width 2 true cm\kern 2.6\p@}

\long\def\@makefntext#1{\@setpar{\@@par\@tempdima \hsize
  \advance\@tempdima-1em\parshape \@ne 1em\@tempdima}\par
  \parindent 1em\noindent \hbox to \z@{\hss$^{\@thefnmark}$\ }#1}

\setcounter{topnumber}{2}
\def\topfraction{.9}
\setcounter{bottomnumber}{1}
\def\bottomfraction{.3}
\setcounter{totalnumber}{3}
\def\textfraction{.15}
\def\floatpagefraction{.85}
\setcounter{dbltopnumber}{2}
\def\dbltopfraction{.85}
\def\dblfloatpagefraction{.85}

\long\def\@makecaption#1#2{
 \vskip 10pt
 \setbox\@tempboxa\hbox{{\bf #1} #2}
 \ifdim \wd\@tempboxa >\hsize \unhbox\@tempboxa\par \else \hbox
to\hsize{\hfil\box\@tempboxa\hfil}
 \fi\vskip5pt}

\long\def\@caption#1[#2]#3{\addcontentsline{\csname
  ext@#1\endcsname}{#1}{\protect\numberline{\csname
  the#1\endcsname}{\ignorespaces #2}}\par
  \begingroup
    \@parboxrestore
    \@makecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par
  \endgroup}

\newcounter{figure}
\def\thefigure{\@arabic\c@figure}

\def\fps@figure{htbp}
\def\ftype@figure{1}
\def\ext@figure{lof}
\def\fnum@figure{\figurename\thefigure.}
\def\figure{\small\rm\@float{figure}}
\def\endfigure{\vskip-5pt\end@float}
\@namedef{figure*}{\@dblfloat{figure}}
\@namedef{endfigure*}{\end@dblfloat}

\newcounter{table}
\def\thetable{\@arabic\c@table}
\def\fps@table{htbp}
\def\ftype@table{2}
\def\ext@table{lot}
\def\fnum@table{\tablename\thetable.}
\def\table{\small\rm\@float{table}}
\let\endtable\end@float
\@namedef{table*}{\@dblfloat{table}}
\@namedef{endtable*}{\end@dblfloat}

% LaTeX does not provide a command to enter the authors institute
% addresses. The \institute command is defined here.

\newcounter{@inst}
\newcounter{@auth}

\def\institute#1{\gdef\@institute{#1}}

\def\institutename{\par
 \begingroup
 \parskip=\z@
 \parindent=\z@
 \setcounter{@inst}{1}%
 \def\and{\par\stepcounter{@inst}%
 \noindent$^{\the@inst}$\enspace\ignorespaces}%
 \setbox0=\vbox{\def\thanks##1{}\@institute}%
 \ifnum\c@@inst=1\relax
 \else
   \setcounter{footnote}{\c@@inst}%
   \setcounter{@inst}{1}%
   \noindent$^{\the@inst}$\enspace
 \fi
 \ignorespaces
 \@institute\par
 \endgroup}

\def\@thanks{}

\def\@fnsymbol#1{\ifcase#1\or\star\or{\star\star}\or{\star\star\star}%
   \or \dagger\or \ddagger\or
   \mathchar "278\or \mathchar "27B\or \|\or **\or \dagger\dagger
   \or \ddagger\ddagger\else\@ctrerr\fi\relax}

\def\inst#1{\unskip$^{#1}$}

\def\subtitle#1{\gdef\@subtitle{#1}}
\def\@subtitle{}

\def\maketitle{\par
 \begingroup
 \parindent=\z@
 \def\thefootnote{\fnsymbol{footnote}}
 \if@twocolumn
 \twocolumn[\@maketitle]
 \else \newpage
 \global\@topnum\z@ \@maketitle \fi\thispagestyle{empty}\@thanks
 \endgroup
 \let\maketitle\relax
 \let\@maketitle\relax
 \gdef\@thanks{}\gdef\@author{}\gdef\@title{}\gdef\@subtitle{}%
 \let\thanks\relax}

\def\@maketitle{\newpage
 \begin{center}%
 {\LARGE \bf\boldmath
  \pretolerance=10000
  \@title \par}\vskip .8cm
\if!\@subtitle!\else {\Large \bf\boldmath
  \vskip -.65cm
  \pretolerance=10000
  \@subtitle \par}\vskip .8cm\fi
{\normalsize\rm\lineskip .5em
\@author\vskip.35cm}
 {\small\rm\institutename}
 \end{center}%
 }

\mark{{}{}}

% Define `abstract' environment
\def\abstract{%
\list{}{\advance\topsep by0.35cm\relax\small\rm
 \leftmargin=1cm
 \labelwidth=\z@
 \listparindent=\z@
 \itemindent\listparindent
 \rightmargin\leftmargin}\item[\hskip\labelsep\bf\abstractname]}
\let\endabstract=\endlist
\def\quote{\list{}{\rightmargin\leftmargin}\item[]}
\let\endquote=\endlist

\def\ps@headings{\def\@evenhead{}%
\let\@oddhead\@evenhead
\let\@evenfoot\@evenhead
\let\@oddfoot\@evenhead
\def\sectionmark##1{}%
\def\subsectionmark##1{}}
\def\ps@myheadings{\let\@mkboth\@gobbletwo
\def\@oddhead{\hbox{}\small\rm\rightmark \hfil\thepage}%
\def\@oddfoot{}\def\@evenhead{\small\rm\thepage\hfil
\leftmark\hbox {}}%
\def\@evenfoot{}\def\sectionmark##1{}\def\subsectionmark##1{}}

\def\today{\ifcase\month\or
 January\or February\or March\or April\or May\or June\or
 July\or August\or September\or October\or November\or December\fi
 \space\number\day, \number\year}

\ps@headings \pagenumbering{arabic} \onecolumn
\if@twoside\else\raggedbottom\fi

% new environments and theorems
% borrowed form the LTMP-style of Springer-Verlag
% designed by Dr. Christoph Ender
%
% define the new theorem like environments
% define a new style of environments where it is possible to define
% the font % used as the theorem name and the fontfamily for the text.
%
% \newstytheorem{name}{thefont}{txtfont}{Text}[Counter]
% \newstytheorem{name}{thefont}{txtfont}[oldname]{Text}
%
% #1 - name of theorem
% #2 - theorem font
% #3 - text font
%
\def\newstytheorem#1#2#3{%
\@ifnextchar[{\che@othm{#1}{#2}{#3}}{\che@nthm{#1}{#2}{#3}}}
%
% #1 - name of theorem
% #2 - theorem font
% #3 - text font
% #4 - text string of thorem name
%
\def\che@nthm#1#2#3#4{%
\@ifnextchar[{\che@xnthm{#1}{#2}{#3}{#4}}{\che@ynthm{#1}{#2}{#3}{#4}}}
%
% #1 - name of theorem
% #2 - theorem font
% #3 - text font
% #4 - text string of thorem name
% #5 - add theorem counter to reset list of another counter
%
\def\che@xnthm#1#2#3#4[#5]{\expandafter
\@ifdefinable\csname #1\endcsname
{\@definecounter{#1}\if@envcountreset\@addtoreset{#1}{#5}\fi
\expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}%
\global\@namedef{#1}{\che@thm{#1}{#4}{#2}{#3}}\global
\@namedef{end#1}{\@endtheorem}}}
%
% #1 - name of theorem
% #2 - theorem font
% #3 - text font
% #4 - text string of thorem name
%
\def\che@ynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname
{\@definecounter{#1}%
\expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}%
\global\@namedef{#1}{\che@thm{#1}{#2}{#3}{#4}}\global
\@namedef{end#1}{\@endtheorem}}}
%
% change oldthm if oldname in specification is '*'
% then don't use a counter
% #1 - countername
% #2 - theorem font
% #3 - text font
% #4 - counter used
% #5 - string containing theorem name to print
%
\def\che@othm#1#2#3[#4]#5{\expandafter\@ifdefinable
\csname#1\endcsname%
{\@@othm@{#1}{#2}{#3}{#4}{#5}\global\@namedef{end#1}{\@endtheorem}}}
%
\def\@@othm@#1#2#3#4#5{\if *#4{\global\@namedef{the#1}{\relax}
\global\@namedef{#1}{\@bthm@{}{#5}{#2}{#3}}}\else
{\global\@namedef{the#1}{\@nameuse{the#4}}% define the counter
\global\@namedef{#1}{\che@thm{#4}{#5}{#2}{#3}}}\fi}
%
% new defs for theorem environment che 17-MAR-1989
% it improves the option possible
%
% #1 - countername  = theorem name
% #2 - string containing theorem name to print
% #3 - theorem font
% #4 - text font
\def\che@thm#1#2#3#4{\@ifnextchar({\@athm{#1}{#2}{#3}{#4}}{%
\@ifnextchar *{\@bthm{#1}{#2}{#3}{#4}}%
{\@@thm{#1}{#2}{#3}{#4}}}}
%
% \begin{thm}(A.1)[test]      results in:
% \end{thm}                               thm A.1 (test) ....
% #1 - theorem
% #2 - string of theorem name
% #3 - font for theorem name and label
% #4 - Text font
% #5 - is the new label
% #6 - optional string
%
\def\@athm#1#2#3#4(#5){\@ifnextchar[{%
\@aythm{#1}{#2}{#3}{#4}{#5}}{\@axthm{#1}{#2}{#3}{#4}{#5}}}
\def\@axthm#1#2#3#4#5{\@@locthmlab{#1}{#5}%
\@begintheorem{#2}{#5}{#3}{#4}\ignorespaces}
\def\@aythm#1#2#3#4#5[#6]{\@@locthmlab{#1}{#5}%
\fuh@opargbegintheorem{#2}{#5}{#6}{#3}{#4}\ignorespaces}
%
% \begin{thm}*[xytest]        results in:
% \end{thm}                               thm (xytest) ....
% #1 - theorem
% #2 - string of theorem name
% #3 - font for theorem name and label
% #4 - Text font
% #5 - optional string
%
\def\@bthm@#1#2#3#4{\@ifnextchar[{\@bythm{#1}{#2}{#3}{#4}}{%
\@bxthm{#1}{#2}{#3}{#4}}}
\def\@bthm#1#2#3#4*{\@ifnextchar[{\@bythm{#1}{#2}{#3}{#4}}{%
\@bxthm{#1}{#2}{#3}{#4}}}
\def\@bxthm#1#2#3#4{\if !#1!\relax\else\@@locthmlab{#1}{}\fi
\@@begintheorem{#2}{#3}{#4}\ignorespaces}
\def\@bythm#1#2#3#4[#5]{%
\@@opargbegintheorem{#2}{#3}{#4}{#5}\ignorespaces}
%
% define local label
%   if no number or a user specified label occured
%
\def\@@locthmlab#1#2{\expandafter\def\csname the#1\endcsname{#2}
\let\@chetempa\protect\def\protect{\noexpand\protect\noexpand}%
\edef\@currentlabel{\csname p@#1\endcsname\csname the#1\endcsname}%
\let\protect\@chetempa}
%
% #1 - counter = theorem name
% #2 - string with name
% #3 - font for theorem name and label
% #4 - font for text
\def\@@thm#1#2#3#4{\refstepcounter
    {#1}\@ifnextchar[{\che@ythm{#1}{#2}{#3}{#4}}{%
    \che@xthm{#1}{#2}{#3}{#4}}}
%
\def\che@xthm#1#2#3#4{\che@begintheorem{#2}{\csname
the#1\endcsname}{#3}{#4}\ignorespaces}
\def\che@ythm#1#2#3#4[#5]{\che@opargbegintheorem{#2}{\csname
       the#1\endcsname}{#5}{#3}{#4}\ignorespaces}
%
% #1 - name of theorem
% #2 - label string
% #3 - font for name and lable
% #4 - text fomt
%
\def\che@begintheorem#1#2#3#4{#4\trivlist\item[\hskip\labelsep
#3#1\ts #2.]}
%
% #1 - name of theorem
% #2 - label string
% #3 - additonal text
% #4 - font for name and lable
% #5 - text fomt
%
\def\che@opargbegintheorem#1#2#3#4#5{#5\trivlist
\item[\hskip\labelsep#4#1\ts #2\ #3.]}
%
\def\fuh@opargbegintheorem#1#2#3{\it \trivlist
      \item[\hskip \labelsep{\bf #1\ #2\ (#3).}]}
%
\def\@@begintheorem#1#2#3{#3\trivlist\item[\hskip\labelsep
#2#1.]}
\def\@@opargbegintheorem#1#2#3#4{#3\trivlist\item[\hskip\labelsep
#2#1 #4.]}

\if@deutsch
\newstytheorem{theorem}{\bf}{\it}{Theorem}[section]
\newstytheorem{example}{\it}{\rm}{Beispiel}[section]
\newstytheorem{proposition}{\bf}{\it}[theorem]{Proposition}
\newstytheorem{corollary}{\bf}{\it}[theorem]{Korollar}
\newstytheorem{lemma}{\bf}{\it}[theorem]{Lemma}
\newstytheorem{proof}{\it}{\rm}[*]{Beweis}
\newstytheorem{definition}{\bf}{\rm}[theorem]{Definition}
\newstytheorem{remark}{\it}{\rm}[*]{Anmerkung}
\newstytheorem{exercise}{\it}{\rm}[theorem]{\"{U}bung}
\newstytheorem{problem}{\it}{\rm}[theorem]{Problem}
\newstytheorem{solution}{\it}{\rm}[theorem]{L\"{o}sung}
\newstytheorem{note}{\it}{\rm}[theorem]{Hinweis}
\newstytheorem{question}{\it}{\rm}[theorem]{Frage}
\else
\newstytheorem{theorem}{\bf}{\it}{Theorem}[section]
\newstytheorem{example}{\it}{\rm}{Example}[section]
\newstytheorem{proposition}{\bf}{\it}[theorem]{Proposition}
\newstytheorem{corollary}{\bf}{\it}[theorem]{Corollary}
\newstytheorem{lemma}{\bf}{\it}[theorem]{Lemma}
\newstytheorem{proof}{\it}{\rm}[*]{Proof}
\newstytheorem{definition}{\bf}{\rm}[theorem]{Definition}
\newstytheorem{remark}{\it}{\rm}[*]{Remark}
\newstytheorem{exercise}{\it}{\rm}[theorem]{Exercise}
\newstytheorem{problem}{\it}{\rm}[theorem]{Problem}
\newstytheorem{solution}{\it}{\rm}[theorem]{Solution}
\newstytheorem{note}{\it}{\rm}[theorem]{Note}
\newstytheorem{question}{\it}{\rm}[theorem]{Question}
\fi

\def\squareforqed{\hbox{\rlap{$\sqcap$}$\sqcup$}}
\def\qed{\ifmmode\squareforqed\else{\unskip\nobreak\hfil
\penalty50\hskip1em\null\nobreak\hfil\squareforqed
\parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi}

\def\getsto{\mathrel{\mathchoice {\vcenter{\offinterlineskip
\halign{\hfil
$\displaystyle##$\hfil\cr\gets\cr\to\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr\gets
\cr\to\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr\gets
\cr\to\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
\gets\cr\to\cr}}}}}
\def\lid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr
\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr
\noalign{\vskip1pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
<\cr
\noalign{\vskip0.9pt}=\cr}}}}}
\def\gid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr
\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr
\noalign{\vskip1pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr
\noalign{\vskip0.9pt}=\cr}}}}}
\def\grole{\mathrel{\mathchoice {\vcenter{\offinterlineskip
\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\noalign{\vskip-1pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
>\cr\noalign{\vskip-1pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
>\cr\noalign{\vskip-0.8pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr\noalign{\vskip-0.3pt}<\cr}}}}}
\def\bbbr{{\rm I\!R}} %reelle Zahlen
\def\bbbm{{\rm I\!M}}
\def\bbbn{{\rm I\!N}} %natuerliche Zahlen
\def\bbbf{{\rm I\!F}}
\def\bbbh{{\rm I\!H}}
\def\bbbk{{\rm I\!K}}
\def\bbbp{{\rm I\!P}}
\def\bbbone{{\mathchoice {\rm 1\mskip-4mu l} {\rm 1\mskip-4mu l}
{\rm 1\mskip-4.5mu l} {\rm 1\mskip-5mu l}}}
\def\bbbc{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm C$}\hbox{\hbox
to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle\rm C$}\hbox{\hbox
to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle\rm C$}\hbox{\hbox
to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm C$}\hbox{\hbox
to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}}}
\def\bbbq{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm
Q$}\hbox{\raise
0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle\rm Q$}\hbox{\raise
0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle\rm Q$}\hbox{\raise
0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm Q$}\hbox{\raise
0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}}}
\def\bbbt{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm
T$}\hbox{\hbox to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle\rm T$}\hbox{\hbox
to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle\rm T$}\hbox{\hbox
to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm T$}\hbox{\hbox
to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}}}
\def\bbbs{{\mathchoice
{\setbox0=\hbox{$\displaystyle     \rm S$}\hbox{\raise0.5\ht0\hbox
to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox
to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle        \rm S$}\hbox{\raise0.5\ht0\hbox
to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox
to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle      \rm S$}\hbox{\raise0.5\ht0\hbox
to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox
to0pt{\kern0.5\wd0\vrule height0.45\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm S$}\hbox{\raise0.5\ht0\hbox
to0pt{\kern0.4\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox
to0pt{\kern0.55\wd0\vrule height0.45\ht0\hss}\box0}}}}
\def\bbbz{{\mathchoice {\hbox{$\sf\textstyle Z\kern-0.4em Z$}}
{\hbox{$\sf\textstyle Z\kern-0.4em Z$}}
{\hbox{$\sf\scriptstyle Z\kern-0.3em Z$}}
{\hbox{$\sf\scriptscriptstyle Z\kern-0.2em Z$}}}}
\def\ts{\thinspace}

\if@deutsch
\def\typeset{\vfill\small\noindent Dieser Artikel wurde mit
dem \LaTeX\ Makro-Paket und dem LLNCS-Style formatiert.\par}
\else
%\def\typeset{\vfill\small\noindent This article was processed using
%the \LaTeX\ macro package with LLNCS style\par}
\def\typeset{\vfill\small\noindent{\ }}
\fi

\def\enddocument{\par\typeset
\@checkend{document}\clearpage\begingroup
\if@filesw \immediate\closeout\@mainaux
\def\global\@namedef##1##2{}\def\newlabel{\@testdef r}%
\def\bibcite{\@testdef b}\@tempswafalse\makeatletter\input \jobname.aux
\if@tempswa \@warning{Label(s) may have changed. Rerun to get
cross-references right}\fi\fi\endgroup\deadcycles\z@\@@end}

