108 lines
3.4 KiB
TeX
108 lines
3.4 KiB
TeX
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% Style file for CS5311 "Theory of Computation" documents
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% Charles Wallace
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% These style settings are what I use to format the lecture notes and homework assignments.
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% Feel free to use as much (or as little) of them as you like.
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\usepackage{amsmath}
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\usepackage{amsthm}
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\usepackage{latexsym}
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\usepackage{fullpage,parskip,paralist}
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\usepackage{amsmath,amsthm,amssymb}
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\usepackage{graphicx}
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\ifdefined\nosol
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\newcommand{\sol}[1]{}
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\newcommand{\soltitle}{}
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\else
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\newcommand{\sol}[1]{{\bf Solution.} #1}
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\newcommand{\soltitle}{: Solutions}
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\fi
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\newcommand{\thetitle}[1]{\title{#1\soltitle}}
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\author{}
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\date{CS5311, Theory of Computation}
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% \ie, \eg: the abbreviations the way they are supposed to be written
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\newcommand{\ie}{{\em i.e.,}}
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\newcommand{\eg}{{\em e.g.,}}
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% These set common formats for various kinds of names
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% \prob{P}: name of problem/language P
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\newcommand{\prob}[1]{\mbox{\bf #1}}
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% \pprob{P}{M}: problem P restricted to machine class M
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\newcommand{\pprob}[2]{\mbox{$\prob{#1}_{\prob{\tiny #2}}$}}
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% \prog{M}: name of program/machine M
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\newcommand{\prog}[1]{\mbox{\tt #1}}
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% \enc{M}: string encoding of machine M
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\newcommand{\enc}[1]{\mbox{[\prog{#1}]}}
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% \lang{M}: language accepted by machine M
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\newcommand{\lang}[1]{\mbox{\bf L(\prog{#1})}}
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% definition environment (unnumbered)
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\theoremstyle{definition}
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\newtheorem*{definition}{Definition}
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% numbered environments: theorem, proof, lemma, corollary, claim
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\newtheorem{theorem}{Theorem}
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\newtheorem{lemma}{Lemma}
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\newtheorem{corollary}{Corollary}
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\newtheorem{claim}{Claim}
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% Proof opening statement
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\newcommand{\prf}{{\em Proof.}}
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\newcommand{\prfout}{{\em Proof outline.}}
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% \code{L}{P}{I}{C}: Turing Machine code (as a box containing formatted text)
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% L: horizontal length of box
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% P: name of program
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% I: names of inputs
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% C: program code
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\newcommand{\code}[4]{\fbox{\parbox{#1}
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{\prog{#2}\hfill (Input: #3)
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\begin{enumerate}
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#4
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\end{enumerate}}}}
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% some common problems
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\newcommand{\atm}{\pprob{A}{TM}}
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\newcommand{\etm}{\pprob{E}{TM}}
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\newcommand{\alltm}{\pprob{All}{TM}}
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\newcommand{\acfl}{\pprob{A}{CFL}}
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\newcommand{\allcfl}{\pprob{All}{CFL}}
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\newcommand{\areg}{\pprob{A}{RL}}
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\newcommand{\allreg}{\pprob{All}{RL}}
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\newcommand{\anfa}{\pprob{A}{NFA}}
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\newcommand{\adfa}{\pprob{A}{DFA}}
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% \bigo{T}: big-O of term T
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\newcommand{\bigo}[1]{\mbox{O$(#1)$}}
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% \expbigo{T}: 2^(big-O of term T)
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\newcommand{\expbigo}[1]{\mbox{$2^{\mbox{O$(#1)$}}$}}
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% \bigom{T}: big-Omega of term T
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\newcommand{\bigom}[1]{\mbox{$\Omega(#1)$}}
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% time/space complexity terms
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\newcommand{\TIME}[1]{\mbox{TIME$(#1)$}}
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\newcommand{\NTIME}[1]{\mbox{NTIME$(#1)$}}
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\newcommand{\SPACE}[1]{\mbox{SPACE$(#1)$}}
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\newcommand{\NSPACE}[1]{\mbox{NSPACE$(#1)$}}
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% some common complexity classes
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\newcommand{\PTIME}{\mbox{P}}
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\newcommand{\NPTIME}{\mbox{NP}}
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\newcommand{\EXPTIME}{\mbox{EXPTIME}}
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\newcommand{\PSPACE}{\mbox{PSPACE}}
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\newcommand{\NPSPACE}{\mbox{NPSPACE}}
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\newcommand{\LSPACE}{\mbox{L}}
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\newcommand{\NLSPACE}{\mbox{NL}}
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\newcommand{\coNLSPACE}{\mbox{coNL}}
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\newcommand{\NC}{\mbox{NC}}
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\newcommand{\NPcomplete}{\NPTIME-complete}
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% \polyreduce{P}{Q} polynomial-time reduction relation
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\newcommand{\polyreduce}[2]{$\prob{#1}\leq_{\mbox{\small P}}\prob{#2}$}
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% \logreduce{P}{Q}: log-space reduction relation
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\newcommand{\logreduce}[2]{$\prob{#1}\leq_{\mbox{\small L}}\prob{#2}$}
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\newcommand{\gad}{\mathbf{Gadget}}
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\newcommand{\domino}[2]
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{\begin{tabular}{|l|} \hline $#1$\\ \hline $#2$ \\ \hline \end{tabular}}
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