+\def\qeditem{{\parfillskip=0pt\hfill\rlap{\hskip\rightskip\llap{$\spadesuit$}}\par}}
+\def\qedmath{\eqno{\spadesuit}}
+\def\FIXME#1{\>{\bo TODO:} #1}
+\def\symdiff{\mathbin{\Delta}}
+\def\rack#1#2{\setbox0=\hbox{#1}\hbox to \wd0{#2}}
+\def\o#1{\accent23 #1}
+\def\mst{\mathop{\rm mst}}
+\def\msf{\mathop{\rm msf}}
+\def\deg{\mathop{\rm deg}}
+\def\timesalpha{\mskip2mu\alpha}
+\def\timesbeta{\mskip2mu\beta}
+\def\tower{\mathbin\uparrow}
+\def\Forb{{\rm Forb}}
+\def\minorof{\preccurlyeq}
+\def\per{\mathop{\rm per}}
+\def\poly{\mathop{\rm poly}}
+\def\E{{\bb E}}
+\def\crpt{\mathbin{\Uparrow}}
+\def\C{{\cal C}}
+
+\def\brk{\hfil\break}
+
+% Bit strings
+\def\0{{\bf 0}}
+\def\1{{\bf 1}}
+\def\(#1){\mathord{\left<#1\right>}}
+
+% Bitwise operations
+\def\shl{\mathbin{<\!<}}
+\def\shr{\mathbin{>\!>}}
+\def\bop#1{\mathbin{\hbox{\sc #1}}}
+\def\band{\bop{and}}
+\def\bor{\bop{or}}
+\def\bxor{\bop{xor}}
+\def\bnot{\mathop{\hbox{\sc not}}}
+
+% A reversed version of \ddots with extra space at the top to get good alignment of exponents.
+\def\rddots{\mathinner{\mkern1mu\raise\p@\vbox{\kern7\p@\hbox{.}}\mkern2mu
+ \raise4\p@\hbox{.}\mkern2mu\raise7\p@\hbox{.}\raise11\p@\hbox{}\mkern1mu}}