defs.tex

   1 \usepackage{amssymb,amsmath}
   2
   3 % From kolmbook:
   4 \usepackage{rusaddlat} % mod.
   5 %\usepackage{fullpage}
   6 %\usepackage{local}              % local.sty
   7 \usepackage{showlabels}
   8 \usepackage{xspace}
   9
  10 % Macros:
  11
  12 \newcommand*{\defStyle}[1]{#1}
  13 \newcommand*{\tD}[2]{\emph{\defStyle{#1}}\footnote{óÍ. ÏÐÒ.~\ref{#2}}}
  14 \newcommand*{\tDJust}[1]{\emph{\defStyle{#1}}}
  15 \newcommand*{\tING}[1]{\textbf{\emph{\defStyle{#1}}}}
  16 \newcommand*{\tND}[2]{\textsl{\defStyle{#1}}\footnote{óÍ. ÏÐÒ.~\ref{#2}}}
  17 \newcommand*{\tNDNo}[1]{\textsl{\defStyle{#1}}}
  18
  19 %\newcommand*{\Emph}[1]{\textbf{\underline{#1}}}
  20 \newcommand*{\Emph}[1]{\underline{\emph{#1}}}
  21
  22 \newcommand*{\implic}{\rightarrow}
  23 \newcommand*{\equivc}{\leftrightarrow}
  24
  25 \newcommand*{\iffdef}{\overset{\text{\tiny def}}{\iff}}
  26
  27 \newcommand*{\eqdef}{\stackrel{\text{\upshape\tiny def}}{=}}
  28 \newcommand*{\equivdef}{\overset{\text{\tiny def}}{\longleftrightarrow}}
  29 %\newcommand*{\equivdef}{\rightleftharpoons}
  30
  31
  32 %\newcommand*{\IFF}{{\upshape\textsc{ÔÉÔÔË\ }}}
  33 \newcommand*{\IFF}{\textsc{ÔÉÔÔË\ }}
  34
  35 %\newcommand*{\Equiv}{\sim}
  36 \newcommand*{\size}[1]{\left\lvert#1\right\rvert}
  37 %\newcommand*{\Size}[1]{\left\lVert#1\right\rVert}
  38
  39 \newcommand*{\place}{\underline{\phantom{x}}}
  40
  41 \usepackage{ifthen}
  42
  43 \usepackage{amsthm}
  44 %\usepackage{theorem}
  45 \newtheorem{theorem}{ôÅÏÒÅÍÁ}[chapter]
  46 \newtheorem{proposition}[theorem]{õÔ×ÅÒÖÄÅÎÉÅ}
  47 \newtheorem{corollary}[theorem]{óÌÅÄÓÔ×ÉÅ}
  48 \newtheorem{oProblem}[theorem]{ïÔËÒÙÔÁÑ ÐÒÏÂÌÅÍÁ}%[chapter]
  49 \theoremstyle{definition}
  50 \newtheorem{definition}[theorem]{ïÐÒÅÄÅÌÅÎÉÅ}%[chapter]
  51 %\theoremstyle{ascet}
  52 %\swapnumbers
  53 \theoremstyle{remark}
  54 \newtheorem{remark}[theorem]{úÁÍÅÞÁÎÉÅ}%[chapter]
  55 \newtheorem{question}[theorem]{÷ÏÐÒÏÓ}%[chapter]
  56 \newtheorem{example}[theorem]{ðÒÉÍÅÒ}
  57 \newtheorem{application}[theorem]{úÁÍÅÞÁÎÉÅ Ï ÐÒÉÍÅÎÅÎÉÉ Ë
  58   ÉÓÓÌÅÄÏ×ÁÎÉÀ ÐÒÏÇÒÁÍÍ}
  59
  60 \usepackage{multirow}
  61 \usepackage{hhline}
  62
  63 \usepackage[mathscr]{eucal}
  64 % Notation:
  65
  66 \newcommand*{\transp}[1]{{#1}^{\mathrm T}}
  67
  68 \newcommand*{\bt}[1]{\mathsf{#1}}
  69
  70 \newcommand*{\srtermStyle}[1]{\underline{#1}}
  71 \newcommand*{\srterm}[1]{\srtermStyle{#1}}
  72 % alias:
  73 \newcommand*{\matrOfSize}[3]{\underset{{\tiny #2 \times #3}}{#1}}
  74 \newcommand*{\smatrStyle}[1]{\underline{\underline{#1}}}
  75 \newcommand*{\smatr}[3]{\matrOfSize{\smatrStyle{#1}}{#2}{#3}}
  76 \newcommand*{\smatrAny}[1]{\smatrStyle{#1}}
  77 \newcommand*{\matrt}[3]{\matrOfSize{#1}{#2}{#3}}
  78
  79 \newcommand*{\class}[1]{\mathbf{#1}}
  80
  81 \newcommand*{\metaconstSemStyle}[1]{{\normalfont\textsf{#1}}}
  82 \newcommand*{\metaconstSem}[1]{\text{{\normalfont\metaconstSemStyle{#1}}}}
  83 \newcommand*{\DeclareMetaconstSem}[2]{\newcommand*{#1}{\metaconstSem{#2}}}
  84
  85 \newcommand*{\DeclareCategory}[2]{\newcommand*{#1}{\ensuremath{\metaconstSem{#2}}\xspace}}
  86 \DeclareCategory{\Mon}{Mo}
  87 \newcommand*{\Sr}{\ensuremath{\metaconstSem{Sr}}\xspace}
  88 \newcommand*{\ISr}{\ensuremath{\metaconstSem{ISr}}\xspace}
  89 \newcommand*{\KA}{\ensuremath{\metaconstSem{KA}}\xspace}
  90 \newcommand*{\KAT}{\ensuremath{\metaconstSem{KAT}}\xspace}
  91 \newcommand*{\KAc}{\ensuremath{\metaconstSem{KA*}}\xspace}
  92 \newcommand*{\KATc}{\ensuremath{\metaconstSem{KAT*}}\xspace}
  93 \newcommand*{\RKA}{\ensuremath{\metaconstSem{RKA}}\xspace}
  94 \newcommand*{\RKAT}{\ensuremath{\metaconstSem{RKAT}}\xspace}
  95
  96 % parametrized:
  97 \newcommand*{\Reg}{\metaconstSem{Reg}}
  98
  99 \usepackage{stmaryrd}
 100 \newcommand*{\trReg}{\metaconstSem{Tr}}
 101 \newcommand*{\trI}[1]{\left\llbracket#1\right\rrbracket}
 102 \newcommand*{\trIP}{\trI{\place}}
 103 \newcommand*{\TRACE}{\ensuremath{\metaconstSem{TRACE}}\xspace}
 104 \newcommand*{\TRACET}{\ensuremath{\metaconstSem{TRACET}}\xspace}
 105
 106 \newcommand*{\relReg}{\metaconstSem{Rel}}
 107 \newcommand*{\relI}[1]{\left[#1\right]}
 108 \newcommand*{\relIP}{\relI{\place}}
 109 \newcommand*{\REL}{\ensuremath{\metaconstSem{REL}}\xspace}
 110 \newcommand*{\RELT}{\ensuremath{\metaconstSem{RELT}}\xspace}
 111 %\DeclareMetaconstSem{\ResultsForAll}{ResultsForAll}
 112 %\DeclareMetaconstSem{\AcceptsForAll}{AcceptsForAll}
 113 \DeclareMetaconstSem{\RSIMPLE}{RSIMPLE}
 114 %\DeclareMetaconstSem{\RFTAPES}{RFTAPES}
 115
 116 % homomorphism:
 117 \DeclareMathOperator{\Ext}{\metaconstSemStyle{Ext}}
 118
 119 % functor:
 120 \DeclareMathOperator{\REG}{\metaconstSemStyle{REG}}
 121
 122 \newcommand{\standardSr}[1]{\mathbb{#1}}
 123 \newcommand{\bbR}{\standardSr{R}}
 124 \newcommand{\bbN}{\standardSr{N}}
 125 \newcommand{\bbZ}{\standardSr{Z}}
 126 %\newcommand{\bbB}{\standardSr{B}}
 127
 128 % syntactic:
 129 \newcommand*{\metaconstSyntStyle}[1]{\textrm{#1}}
 130 \newcommand*{\metaconstSynt}[1]{\text{{\normalfont\metaconstSyntStyle{#1}}}}
 131 \newcommand*{\DeclareMetaconstSynt}[2]{\newcommand*{#1}{\metaconstSynt{#2}}}
 132
 133 \newcommand*{\RExp}{\metaconstSynt{RExp}}
 134 \newcommand*{\MRExp}{\metaconstSynt{MRExp}}
 135 \newcommand*{\NFA}{\metaconstSynt{NFA}}
 136 \newcommand*{\DFA}{\metaconstSynt{DFA}}
 137 \newcommand*{\NPSS}{\metaconstSynt{NPSS}}
 138 \newcommand*{\DPSS}{\metaconstSynt{DPSS}}
 139 \DeclareMetaconstSynt{\AExp}{AExp}
 140
 141 \newcommand*{\kframe}[1]{\mathcal{#1}}
 142 \newcommand*{\fr}[1]{\kframe{#1}} % shorthand
 143 \newcommand*{\kf}[1]{\kframe{#1}} % shorthand
 144 \newcommand*{\autom}[1]{\kframe{#1}}
 145 \newcommand*{\au}[1]{\autom{#1}}
 146 \newcommand*{\structure}[1]{\mathcal{#1}}
 147 \newcommand*{\stru}[1]{\structure{#1}}
 148 \newcommand*{\ka}[1]{\stru{#1}}
 149 \newcommand*{\ba}[1]{\stru{#1}}
 150 \newcommand*{\mo}[1]{\stru{#1}}
 151
 152 \newcommand*{\kaMat}{\ka M}
 153
 154 \newcommand*{\construStyle}[1]{{\normalfont\textsl{#1}}}
 155 \newcommand*{\DeclareConstru}[2]{\DeclareMathOperator{#1}{\construStyle{#2}}}
 156 \DeclareConstru{\Strs}{Strings}
 157 \newcommand*{\eStr}{\epsilon}
 158
 159 \DeclareMathOperator{\Rels}{\construStyle{Relations}}
 160 \newcommand*{\id}{\iota}
 161
 162 \DeclareMathOperator{\Trs}{\construStyle{Traces}}
 163
 164 %\newcommand*{\Strs}[1]{\StrsName(#1)}
 165 %\newcommand*{\Traces}{\construStyle{Traces}}
 166 %\newcommand*{\Relations}{\construStyle{Relations}}
 167
 168
 169 \newcommand*{\Stru}[1]{(#1)}
 170
 171 \newcommand*{\propStyle}[1]{{\normalfont\textbf{#1}}}
 172 \DeclareMathOperator{\First}{\propStyle{first}}
 173 \DeclareMathOperator{\Last}{\propStyle{last}}
 174 \DeclareMathOperator{\Label}{\propStyle{label}}
 175 \DeclareMathOperator{\Length}{\propStyle{length}}
 176 \newcommand*{\Len}[1]{\Length(#1)}
 177
 178 \newcommand*{\trCo}{\diamond}
 179 \newcommand*{\n}[1]{\Bar{#1}}
 180 \newcommand*{\nP}{\n{\place}}
 181
 182 \newcommand*{\ThStyle}[1]{\mathcal{#1}}
 183 \DeclareMathOperator{\EquaOf}{\ThStyle{E}}
 184 \DeclareMathOperator{\HornOf}{\ThStyle{H}}
 185 % aliases:
 186 \newcommand*{\EOf}{\EquaOf}
 187 \newcommand*{\HOf}{\HornOf}
 188 %
 189 \newcommand*{\thclassStyle}[1]{{\normalfont\textbf{#1}}}
 190 \newcommand*{\DeclareThclass}[2]{\newcommand*{#1}{\ensuremath{\thclassStyle{#2}}}\xspace}
 191 \DeclareThclass{\Equa}{Equa}
 192 \DeclareThclass{\MoEqua}{MoEqua}
 193 \DeclareThclass{\ConservEqua}{ConsEqua}
 194 \newcommand*{\ConsEqua}{\ConservEqua}  % alias
 195 \DeclareThclass{\Commut}{Comm}
 196 \newcommand*{\Comm}{\Commut} % alias
 197 \DeclareThclass{\Annihil}{Annih}
 198 \newcommand*{\Annih}{\Annihil} % alias
 199 \DeclareThclass{\Monot}{Monot}
 200 \DeclareThclass{\Shifts}{Shifts}
 201 \DeclareThclass{\Horn}{Horn}
 202 \newcommand*{\thclass}[1]{\mathfrak{#1}} % vars
 203
 204 \newcommand*{\Atoms}{\metaconstSynt{Atoms}}
 205 \newcommand*{\gsCo}{\trCo}
 206 \DeclareMathOperator{\GS}{\construStyle{GS}}
 207
 208 % complexities:
 209 \newcommand*{\complexityStyle}[1]{{\normalfont\textsl{#1}}}
 210 \newcommand*{\complexity}[1]{\ensuremath{\complexityStyle{#1}}\xspace}
 211 \newcommand*{\DeclareComplexity}[2]{\newcommand*{#1}{\complexity{#2}}}
 212 \DeclareComplexity{\PSPACE}{PSPACE}
 213
 214 \newcommand*{\kfOpStyle}[1]{\construStyle{#1}}
 215 \newcommand*{\DeclareKFOp}[2]{\DeclareMathOperator{#1}{\kfOpStyle{#2}}}
 216 \DeclareKFOp{\kfProduct}{Product}
 217 \DeclareKFOp{\kfUnion}{Union}
 218 \DeclareKFOp{\kfLink}{Link}
 219
 220 \newcommand*{\constSymbStyle}[1]{{\normalfont\textsc{#1}}}
 221 \newcommand*{\constSymb}[1]{\constSymbStyle{#1}}
 222 %\newcommand*{\constSymb}[1]{\metaConst{#1}}
 223 \newcommand*{\DeclareConstSymb}[2]{\newcommand*{#1}{\constSymb{#2}}}
 224 \DeclareConstSymb{\Start}{start}
 225 \DeclareConstSymb{\Stop}{stop}
 226
 227 \newcommand*{\mathWord}[1]{\text{\textnormal{#1}}}
 228 \newcommand*{\mword}[1]{\mathWord{#1}} % alias
 229 \newcommand*{\EAutOf}{\EOf^{\mword{Aut}}}
 230 \newcommand*{\HAutOf}{\HOf^{\mword{Aut}}}
 231 \newcommand*{\comm}{\mword{c}}
 232 \newcommand*{\Ecomm}{E_{\comm}}
 233 \newcommand*{\shifts}{\mword{s}}
 234 \newcommand*{\Esh}{E_{\shifts}}
 235
 236 \newcommand*{\Indep}{\mathscr I}
 237 \newcommand*{\IndepBy}[1]{\Indep_{#1}}
 238
 239 \newcommand*{\prStyle}[1]{\text{\textnormal{#1}}}
 240 \newcommand*{\DeclarePr}[2]{\newcommand*{#1}{\prStyle{#2}}}
 241 \DeclarePr{\prINT}{INT}
 242 \DeclarePr{\prINC}{INC}
 243 \DeclarePr{\prEQU}{EQU}
 244 \DeclarePr{\prUNI}{UNI}
 245 \DeclarePr{\prCOM}{COM}
 246 \DeclarePr{\prREC}{REC}
 247
 248 \DeclareConstru{\Frames}{Frames}
 249 \DeclareConstru{\LFrames}{LFrames}
 250 \newcommand*{\leCo}{\sqsubseteq}
 251
 252 %%% Local Variables:
 253 %%% mode: latex
 254 %%% TeX-master: "main"
 255 %%% End: