%%%%%%%%%%%%%%%%%
%IJFCS.sty file
%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%From cfshen Tue Jan  7 16:10:48 1992
% IJFCS.sty style file used for IJFCS
% created on March 5, 1991
% modified on September 27, 1991
% modified on October 31, 1991            % cite, refcite
% modified on August 31, 1998    % cite, refcite

\textwidth=5in
\textheight=8in

%\pagestyle{empty}

\addtolength{\oddsidemargin}{-62pt}
\addtolength{\topmargin}{-62pt}

%%DT changed 4/3/96
%%tenbf is replaced with bf, tenit with it

\font\tenbf=cmbx10
\font\tenrm=cmr10
\font\tenit=cmti10
%\newfont{\ninerm}{cmr9}
%\newfont{\ninebf}{cmbx9}
%\newfont{\nineit}{cmti9}
%\newfont{\eightbf}{cmbx8}
%\newfont{\eightrm}{cmr8}
%\newfont{\eightit}{cmti8}

\parindent=15pt

\newcommand{\symbolfootnote}{\renewcommand{\thefootnote}{\fnsymbol{footnote}}}
\newcommand{\alphfootnote}{
        \setcounter{footnote}{0}
        \renewcommand{\thefootnote}{\alph{footnote}}}

%%%%    new  section commands

\renewcommand{\thesubsection}{\arabic{section}.\arabic{subsection}}
\renewcommand{\thesubsubsection}{\arabic{section}.\arabic{subsection}.\arabic{subsubsection}}

\renewcommand{\section}[1] {\par\vspace{12pt}
        \refstepcounter{section}
        \noindent
        %{\tenbf\thesection. #1}
        {\bf\thesection. #1}
        \par
        \vspace{6pt}
        }
\renewcommand{\subsection}[1] {\par  \vspace{12pt}
        \refstepcounter{subsection}
        \noindent
        %%{\tenit\thesubsection. #1}
        {\it\thesubsection. #1}
        \par
        \vspace{6pt}
        }
\renewcommand{\subsubsection}[1] { \par\vspace{12pt}
        \refstepcounter{subsubsection}
        \noindent
        {\tenrm\thesubsubsection. #1}
        \par
        \vspace{6pt}
        }
\newcommand{\nonumsection}[1] { \par\vspace{12pt}
        \noindent
        %%{\tenbf #1} \par \vspace{6pt}
        {\bf #1} \par \vspace{6pt}
        }
%% --------------------------------------------------------------------

%% new macro to handle appendices
%% added in July 1991, modified in September 1991

\newcounter{appendixc}
\newcounter{subappendixc}[appendixc]
\newcounter{subsubappendixc}[subappendixc]
\renewcommand{\thesubappendixc}{\Alph{appendixc}.\arabic{subappendixc}}
\renewcommand{\thesubsubappendixc}{\Alph{appendixc}.\arabic{subappendixc}.\arabic{subsubappendixc}}
\renewcommand{\appendix}[1] { \par\vspace{12pt}
        \refstepcounter{appendixc}
        \setcounter{figure}{0}
        \setcounter{table}{0}
        \setcounter{lemma}{0}
        \setcounter{theorem}{0}
        \setcounter{corollary}{0}
        \setcounter{definition}{0}
        \setcounter{equation}{0}
        \renewcommand{\thefigure}{\Alph{appendixc}.\arabic{figure}}
        \renewcommand{\thetable}{\Alph{appendixc}.\arabic{table}}
        \renewcommand{\theappendixc}{\Alph{appendixc}}
        \renewcommand{\thelemma}{\Alph{appendixc}.\arabic{lemma}}
        \renewcommand{\thetheorem}{\Alph{appendixc}.\arabic{theorem}}
        \renewcommand{\thedefinition}{\Alph{appendixc}.\arabic{definition}}
        \renewcommand{\thecorollary}{\Alph{appendixc}.\arabic{corollary}}
        \renewcommand{\theequation}{\Alph{appendixc}.\arabic{equation}}
        \noindent
        {\bf Appendix \theappendixc: \ #1} \par \vspace{6pt}
        }
 %%% or {\bf Appendix \theappendixc. #1} \par \vspace{6pt}}

\newcommand{\subappendix}[1] {\par  \vspace{12pt}
        \refstepcounter{subappendixc}
        \noindent
        %%{\tenit\thesubappendixc. #1}
        {\it\thesubappendixc. #1}
        \par
        \vspace{6pt}
        }
\newcommand{\subsubappendix}[1] {\par \vspace{12pt}
        \refstepcounter{subsubappendixc}
        \noindent
        {\tenrm\thesubsubappendixc. #1}
        \par
        \vspace{6pt}
        }
%% --------------------------------------------------------------------

\newtheorem{theorem}{Theorem}
%% or \newtheorem{theorem}{Theorem}[section] which has section number
\newtheorem{lemma}{Lemma}
%% or use \newtheorem{lemma}{Lemma}[section]
\newtheorem{definition}{Definition}
\newtheorem{corollary}{Corollary}
%% users can add on their own new theorem-like environments.
\newtheorem{proposition}{Proposition}
\newtheorem{claim}{Claim}

\newcommand{\ignore}[1]{} 

\newcommand{\proof}[1]{ {\bf Proof.} #1 \hfill$\Box$\par}

%\newcommand{\fcstitle}[1]{{\tenbf #1}}
\newcommand{\fcstitle}[1]{{\bf #1}}
%\newcommand{\authorfont}{\eightrm}
\newcommand{\authorfont}{\footnotesize \rm}
%\newcommand{\addressfont}{\eightit}
\newcommand{\addressfont}{\footnotesize \it}

\newcommand{\textlineskip}{\baselineskip=13pt}
\newcommand{\smalllineskip}{\baselineskip=10pt}
%\newcommand{\footnoteblock}[1]{\footnote{\noindent \smalllineskip \eightrm #1}}

\newcommand{\copyrightheading}{
   \smalllineskip
   \noindent
%   {\eightrm International Journal of Foundations of Computer Science}\\
%   {\eightrm $\copyright$\, World Scientific Publishing Company}\\
   {\footnotesize\rm  International
      Journal of Foundations of Computer Science}\\
   {\footnotesize\rm $\copyright$\, World Scientific Publishing Company}\\
    \vspace{3.7pc} }

%  macro (added on May 6, 1991) for publisher information section
\newcommand{\publisher}[3]{
%  {\eightrm
  {\footnotesize \rm
  \smalllineskip
  Received #1\\
  Revised #2\\
  Communicated by #3\\
  \par
  \vspace{14pt}
  }
}

%%% old marco for abstract block
%\newcommand{\abstractblock}[2]{
   %\centerline{\eightrm ABSTRACT}
   %\par
   %\vspace{6pt}
   %\noindent \hspace{1.5pc} \parbox{4.5in}
        %{\eightrm \baselineskip=10pt \hspace{1pc} #1
        %\par
        %\vspace{6pt}
        %\noindent {\eightit Keywords:} #2 }}

%% new environment for the abstract

\renewenvironment{abstract}[0]
        {\footnotesize\rm
        \begin{center}
         ABSTRACT
    %   \par \vspace{6pt}
        \\ \vspace{6pt}
        \begin{minipage}{4.5in}\smalllineskip
        \hspace{1pc}}{\end{minipage} \end{center}\vspace{-1pt}}

\newcommand{\keywords}[1]{
        \par
        \vspace{6pt}
%        \noindent {\eightit Keywords:} #1 }
        \noindent {\footnotesize \it Keywords:} #1 }



%%%  macro for bibliography
% notice : the following two lines are for old-version users
% It is now valid to use \it and \bf in bibliography enviornment
\newcommand{\bibit}{\nineit}
\newcommand{\bibbf}{\ninebf}

\renewenvironment{thebibliography}[1]
 { %\ninerm
   \small\rm
   \begin{list}{\arabic{enumi}.}
    {\usecounter{enumi} \setlength{\parsep}{0pt}
     \setlength{\topsep}{0pt}
     \setlength{\itemsep}{3pt} \settowidth{\labelwidth}{#1.}
     \sloppy
    }}{\end{list}}

%%  list environments

\newcounter{itemlistc}
\newcounter{romanlistc}
\newcounter{alphlistc}
\newcounter{enumlistc}
\renewcommand{\theromanlistc}{(\roman{romanlistc})} %for ref use
\renewcommand{\thealphlistc}{(\alph{alphlistc})}    %for ref use
\newenvironment{itemlist}
    {   \setcounter{itemlistc}{0}
        \begin{list}{$\bullet$}
        {\usecounter{itemlistc}
         \setlength{\parsep}{0pt}
         \setlength{\topsep}{3pt}
         \setlength{\itemsep}{0pt}}
    }{ \end{list} }
\newenvironment{enumlist}
    {   \setcounter{enumlistc}{0}
        \begin{list}{\arabic{enumlistc}.}
        {\usecounter{enumlistc}
         \setlength{\parsep}{0pt}
         \setlength{\topsep}{3pt}
         \setlength{\itemsep}{0pt}}
    }{ \end{list} }
\newenvironment{romanlist}
    {   \setcounter{romanlistc}{0}
        \begin{list}{(\roman{romanlistc})}
        {\usecounter{romanlistc}
         \setlength{\parsep}{0pt}
         \setlength{\topsep}{3pt}
         \setlength{\itemsep}{0pt}}
    }{ \end{list} }
\newenvironment{alphlist}
    {   \setcounter{alphlistc}{0}
        \begin{list}{(\alph{alphlistc})}
        {\usecounter{alphlistc}
         \setlength{\parsep}{0pt}
         \setlength{\topsep}{3pt}
         \setlength{\itemsep}{0pt}}
    }{ \end{list} }

\topsep=0in
\parsep=0in
\itemsep=0in

%% New figure caption

\newcommand{\fcaption}[1]{
        \refstepcounter{figure}
        %\setbox\@tempboxa = \hbox{\eightrm Fig.~\thefigure. #1}
        \setbox\@tempboxa = \hbox{\footnotesize\rm Fig.~\thefigure. #1}
        \ifdim \wd\@tempboxa > 4in
           {\begin{center}
            %\parbox{4in}{\eightrm \smalllineskip Fig.~\thefigure. #1 }
            \parbox{4in}{\footnotesize\rm \smalllineskip Fig.~\thefigure. #1 }
            \end{center}}
        \else
             {\begin{center}
                %{\eightrm Fig.~\thefigure. #1}
                {\footnotesize\rm Fig.~\thefigure. #1}
              \end{center}}
        \fi
        \vspace{-3pt}}

%% New table caption

\newcommand{\tcaption}[1]{
        \vspace{-2pt}
        \refstepcounter{table}
        %\setbox\@tempboxa = \hbox{\eightrm Table~\thetable. #1}
        \setbox\@tempboxa = \hbox{\footnotesize\rm Table~\thetable. #1}
        \ifdim \wd\@tempboxa > 4in
           {\begin{center}
            %\parbox{4in}{\eightrm \smalllineskip Table~\thetable. #1 }
            \parbox{4in}{\footnotesize\rm \smalllineskip Table~\thetable. #1 }
            \end{center}}
        \else
             {\begin{center}
                %{\eightrm Table~\thetable. #1}
                {\footnotesize\rm Table~\thetable. #1}
              \end{center}}
        \fi}

% this is for old-version user
\newcommand{\capit}{\eightit}

%
%    ACKNOWLEDGEMENT: We Made it!  :)
%
%


% NOTE : SUPERSCRIPT CITES ARE NO LONGER GOING TO BE USED, SO THIS
%        PART IS COMMENTED OUT.
%------------------------------------------------------------------
% This is for superscript cites.  Called by "\cite{x}" or "\citeup{x}".
%
%\def\@citex[#1]#2{\if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi
%  \def\@citea{}\@cite{\@for\@citeb:=#2\do
%    {\@citea\def\@citea{,}\@ifundefined
%       {b@\@citeb}{{\bf ?}\@warning
%       {Citation `\@citeb' on page \thepage \space undefined}}%
%     {\csname b@\@citeb\endcsname}}}{#1}}

%\def\@cite#1#2{{$\null^{#1}$\if@tempswa\typeout
%        {IJCGA warning: optional citation argument ignored: `#2'} \fi}}

%\def\cite{\@ifnextchar [{\@tempswatrue \@citex}{\@tempswafalse\@citex[]}}
%\def\citeup{\cite}

%% This is for normal sized cites like (Ref. 5).  Called by "\cite{x}".

\def\@refcitex[#1]#2{\if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi
  \def\@citea{}\@refcite{\@for\@citeb:=#2\do
    {\@citea\def\@citea{,}\@ifundefined
       {b@\@citeb}{{\bf ?}\@warning
       {Citation `\@citeb' on page \thepage \space undefined}}%
 \hbox{\csname b@\@citeb\endcsname}}}{#1}}

%\def\@refcite#1#2{\null(Ref.~\null{#1\if@tempswa\typeout
%       {IJCGA warning: optional citation argument ignored: `#2'} \fi})}
\def\@refcite#1#2{{#1\if@tempswa\typeout
        {IJCGA warning: optional citation argument ignored: `#2'} \fi}}

\def\refcite{\@ifnextchar[{\@tempswatrue\@refcitex}{\@tempswafalse\@refcitex[]}}



