\documentstyle[12pt]{article}
\setlength{\evensidemargin}{0in}
\setlength{\oddsidemargin}{0in}
%\setlength{\textwidth}{5.75in}
\setlength{\textwidth}{6.75in}
\setlength{\textheight}{9.1in}
%\setlength{\topmargin}{0.5in}
\setlength{\headheight}{0in}
\setlength{\headsep}{0in}

\setlength{\parskip}{\medskipamount}
\addtolength{\baselineskip}{.5\baselineskip}
\setlength{\columnsep}{.8cm}

\def \ni {\noindent}
\newcommand{\bread}{{\bf read}}
\newcommand{\breads}{{\bf read}$\ $}
\newcommand{\bwrite}{{\bf write}}
\newcommand{\bwrites}{{\bf write}$\ $}
\newcommand{\comment}[1]{\marginpar{\scriptsize\raggedright #1}}

%  DELIMITER PAIRS AND MATHEMATICAL FUNCTIONS

\newcommand{\set}[1]{\left\{ #1 \right\}}
\newcommand{\abs}[1]{\left| #1\right|}
\newcommand{\card}[1]{\left| #1\right|}
\newcommand{\bigo}[1]{O\left( #1\right)}
\newcommand{\floor}[1]{\left\lfloor #1 \right\rfloor}
\newcommand{\ceil}[1]{\left\lceil #1 \right\rceil}
\newcommand{\ang}[1]{\left\langle #1 \right\rangle}
\newcommand{\prob}[1]{\Pr\left\{ #1 \right\}}

%  BINARY OPERATION, RELATION, AND ARROW SYMBOLS

\newcommand{\propsubset}
    {\stackrel{\subset}{\scriptscriptstyle \not {\scriptstyle =}}}
\newcommand{\polyred}{\leq_p}
\newcommand{\logred}{\leq_L}
\newcommand{\dhrightarrow}{\rightarrow \hspace*{-15pt} \rightarrow}
\renewcommand{\gets}{\leftarrow}
\newcommand{\manyone}{\leq_{\rm m}}
\newcommand{\turing}{\leq_{\rm T}}
\newcommand{\encode}[1]{\langle #1 \rangle}

%  OTHER MATHEMATICAL SYMBOLS OR CONSTRUCTS

\newcommand{\goesto}[1]{\stackrel{#1}{\rightarrow}}
\newcommand{\pgoesto}[1]{\stackrel{#1}{\dhrightarrow}}
%\newcommand{\js}[2]{\left(\frac{#1}{#2}\right)}
%\newcommand{\sumres}[2]{\sum\limits_{\stackrel{\scriptscriptstyle #2}{\scriptscriptstyle #1}}}
%\newcommand{\prodres}[2]{\prod\limits_{\stackrel{\scriptscriptstyle #2}{\scriptscriptstyle #1}}}

\newcommand{\cents}{\hbox{\rm\rlap/c}}
\newcommand{\half}{\frac{1}{2}}
\def\squarebox#1{\hbox to #1{\hfill\vbox to #1{\vfill}}}
\newcommand{\qed}{\hspace*{\fill}
            \vbox{\hrule\hbox{\vrule\squarebox{.667em}\vrule}\hrule}\smallskip}

%  THEOREM-LIKE ENVIRONMENTS

\newtheorem{THEOREM}{Theorem}
\newenvironment{theorem}{\begin{THEOREM} \hspace{-.85em} {\bf :} \rm}%
                        {\end{THEOREM}}
\newtheorem{CLAIM}[THEOREM]{Claim}
\newenvironment{claim}{\begin{CLAIM} \hspace{-.85em} {\bf :} \rm}%
                      {\end{CLAIM}}
\newtheorem{LEMMA}[THEOREM]{Lemma}
\newenvironment{lemma}{\begin{LEMMA} \hspace{-.85em} {\bf :} \rm}%
                      {\end{LEMMA}}
\newtheorem{COROLLARY}[THEOREM]{Corollary}
\newenvironment{corollary}{\begin{COROLLARY} \hspace{-.85em} {\bf :} \rm}%
                          {\end{COROLLARY}}
\newtheorem{PROPOSITION}[THEOREM]{Proposition}
\newenvironment{proposition}{\begin{PROPOSITION} \hspace{-.85em} {\bf :} \rm}%
                            {\end{PROPOSITION}}
\newenvironment{proof}{\noindent {\bf Proof:} \hspace{.677em}}%
                      {}

%  MACROS FOR ALGORITHMS OR PROGRAMS

%\newcommand{\Begin}{{\bf begin\ }}
%\newcommand{\End}{{\bf end\ }}
\newcommand{\Do}{{\bf do\ }}
%\newcommand{\Od}{{\bf od}}
%\newcommand{\Enddo}{{\bf enddo}}
%\newcommand{\Loop}{{\bf loop\ }}
%\newcommand{\Endloop}{{\bf endloop}}
\newcommand{\For}{{\bf for\ }}
%\newcommand{\Endfor}{{\bf endfor}}
%\newcommand{\Foreach}{{\bf foreach\ }}
%\newcommand{\To}{{\bf to\ }}
\newcommand{\If}{{\bf if\ }}
\newcommand{\Then}{{\bf then\ }}
\newcommand{\Else}{{\bf else\ }}
%\newcommand{\Elif}{{\bf elif\ }}
%\newcommand{\Fi}{{\bf fi}}
%\newcommand{\Endif}{{\bf endif}}
%\newcommand{\While}{{\bf while\ }}
%\newcommand{\Endwhile}{{\bf endwhile}}
\newcommand{\Repeat}{{\bf repeat\ }}
\newcommand{\Until}{{\bf until\ }}
%\newcommand{\Case}{{\bf case\ }}
%\newcommand{\Of}{{\bf of\ }}
%\newcommand{\Procedure}{{\bf procedure\ }}
%\newcommand{\Call}{{\bf call\ }}
%\newcommand{\With}{{\bf with\ }}
%\newcommand{\Imports}{{\bf imports\ }}
%\newcommand{\Var}{{\bf var\ }}
%\newcommand{\Type}{{\bf type\ }}
%\newcommand{\Assert}{{\bf assert\ }}
%\newcommand{\True}{{\rm true}}
%\newcommand{\False}{{\rm false}}

