defs.tex

   1 \usepackage{url}
   2
   3 \usepackage{amssymb,amsmath}
   4
   5 % From kolmbook:
   6 \usepackage{rusaddlat} % mod.
   7 %\usepackage{fullpage}
   8 %\usepackage{local}              % local.sty
   9 \usepackage{xspace}
  10
  11 % Macros:
  12
  13 \newcommand*{\defStyle}[1]{#1}
  14 %\newcommand*{\tD}[2]{\emph{\defStyle{#1}}\footnote{óÍ. ÏÐÒ.~\ref{#2}}}
  15 \newcommand*{\tD}[2]{\emph{\defStyle{#1}}}
  16 \newcommand*{\tDJust}[1]{\emph{\defStyle{#1}}}
  17 \newcommand*{\tING}[1]{\textbf{\emph{\defStyle{#1}}}}
  18 %\newcommand*{\tND}[2]{\textsl{\defStyle{#1}}\footnote{óÍ. ÏÐÒ.~\ref{#2}}}
  19 \newcommand*{\tND}[2]{\textsl{\defStyle{#1}}}
  20 \newcommand*{\tNDNo}[1]{\textsl{\defStyle{#1}}}
  21
  22 %\newcommand*{\Emph}[1]{\textbf{\underline{#1}}}
  23 \newcommand*{\Emph}[1]{\underline{\emph{#1}}}
  24
  25 \newcommand*{\implic}{\rightarrow}
  26 \newcommand*{\equivc}{\leftrightarrow}
  27
  28 \newcommand*{\iffdef}{\overset{\text{\tiny def}}{\iff}}
  29
  30 \newcommand*{\eqdef}{\stackrel{\text{\upshape\tiny def}}{=}}
  31 \newcommand*{\equivdef}{\overset{\text{\tiny def}}{\longleftrightarrow}}
  32 %\newcommand*{\equivdef}{\rightleftharpoons}
  33
  34
  35 %\newcommand*{\IFF}{{\upshape\textsc{ÔÉÔÔË\ }}}
  36 \newcommand*{\IFF}{\textsc{ÔÉÔÔË\ }}
  37
  38 %\newcommand*{\Equiv}{\sim}
  39 \newcommand*{\size}[1]{\left\lvert#1\right\rvert}
  40 %\newcommand*{\Size}[1]{\left\lVert#1\right\rVert}
  41
  42 \newcommand*{\place}{\underline{\phantom{x}}}
  43
  44 \usepackage{ifthen}
  45
  46 \usepackage{amsthm}
  47 %\usepackage{theorem}
  48 \newtheorem{theorem}{ôÅÏÒÅÍÁ}[chapter]
  49 \newtheorem{proposition}[theorem]{õÔ×ÅÒÖÄÅÎÉÅ}
  50 \newtheorem{lemma}[theorem]{ìÅÍÍÁ}
  51 \newtheorem{corollary}[theorem]{óÌÅÄÓÔ×ÉÅ}
  52 \newtheorem*{corollary*}{óÌÅÄÓÔ×ÉÅ}
  53 \newtheorem{oProblem}[theorem]{ïÔËÒÙÔÁÑ ÐÒÏÂÌÅÍÁ}%[chapter]
  54 \theoremstyle{definition}
  55 \newtheorem{definition}[theorem]{ïÐÒÅÄÅÌÅÎÉÅ}%[chapter]
  56 \newtheorem*{definition*}{ïÐÒÅÄÅÌÅÎÉÅ}
  57 %\theoremstyle{ascet}
  58 %\swapnumbers
  59 \theoremstyle{remark}
  60 \newtheorem{remark}[theorem]{úÁÍÅÞÁÎÉÅ}%[chapter]
  61
  62 \newtheorem{questionImpl}[theorem]{÷ÏÐÒÏÓ}%[chapter]
  63 \newenvironment*{question}{\begin{questionImpl}\footnotesize}{\end{questionImpl}}
  64
  65 \newenvironment*{answer}{\begin{proof}[îÁÞÁÌÏ ÏÔ×ÅÔÁ]\footnotesize}{\end{proof}}
  66
  67 \newtheorem{example}[theorem]{ðÒÉÍÅÒ}
  68 \newtheorem{application}[theorem]{úÁÍÅÞÁÎÉÅ Ï ÐÒÉÍÅÎÅÎÉÉ Ë
  69   ÉÓÓÌÅÄÏ×ÁÎÉÀ ÐÒÏÇÒÁÍÍ}
  70
  71 \usepackage{multirow}
  72 \usepackage{hhline}
  73
  74 \usepackage[mathscr]{eucal}
  75 % Notation:
  76
  77 \newcommand*{\transp}[1]{{#1}^{\mathrm T}}
  78
  79 \newcommand*{\bt}[1]{\mathsf{#1}}
  80
  81 \newcommand*{\srtermStyle}[1]{\underline{#1}}
  82 \newcommand*{\srterm}[1]{\srtermStyle{#1}}
  83 % alias:
  84 \newcommand*{\matrOfSize}[3]{\underset{{\tiny #2 \times #3}}{#1}}
  85 \newcommand*{\smatrStyle}[1]{\underline{\underline{#1}}}
  86 \newcommand*{\smatr}[3]{\matrOfSize{\smatrStyle{#1}}{#2}{#3}}
  87 \newcommand*{\smatrAny}[1]{\smatrStyle{#1}}
  88 \newcommand*{\matrt}[3]{\matrOfSize{#1}{#2}{#3}}
  89
  90 \newcommand*{\class}[1]{\mathbf{#1}}
  91
  92 \newcommand*{\metaconstSemStyle}[1]{{\normalfont\textsf{#1}}}
  93 \newcommand*{\metaconstSem}[1]{\text{{\normalfont\metaconstSemStyle{#1}}}}
  94 \newcommand*{\DeclareMetaconstSem}[2]{\newcommand*{#1}{\metaconstSem{#2}}}
  95
  96 \newcommand*{\DeclareCategory}[2]{\newcommand*{#1}{\ensuremath{\metaconstSem{#2}}\xspace}}
  97 \DeclareCategory{\Mo}{Mo}
  98 \newcommand*{\Mon}{\Mo} % alias
  99 \newcommand*{\Sr}{\ensuremath{\metaconstSem{Sr}}\xspace}
 100 \newcommand*{\ISr}{\ensuremath{\metaconstSem{ISr}}\xspace}
 101 \newcommand*{\KA}{\ensuremath{\metaconstSem{KA}}\xspace}
 102 \newcommand*{\KAT}{\ensuremath{\metaconstSem{KAT}}\xspace}
 103 \newcommand*{\KAc}{\ensuremath{\metaconstSem{KA*}}\xspace}
 104 \newcommand*{\KATc}{\ensuremath{\metaconstSem{KAT*}}\xspace}
 105 \newcommand*{\RKA}{\ensuremath{\metaconstSem{RKA}}\xspace}
 106 \newcommand*{\RKAT}{\ensuremath{\metaconstSem{RKAT}}\xspace}
 107
 108 % parametrized:
 109 \newcommand*{\Reg}{\metaconstSem{Reg}}
 110 \newcommand*{\Cons}{\metaconstSem{Cons}}
 111
 112 \usepackage{stmaryrd}
 113 \newcommand*{\trReg}{\metaconstSem{Tr}}
 114 \newcommand*{\trI}[1]{\left\llbracket#1\right\rrbracket}
 115 \newcommand*{\trIP}{\trI{\place}}
 116 \newcommand*{\TRACE}{\ensuremath{\metaconstSem{TRACE}}\xspace}
 117 \newcommand*{\TRACET}{\ensuremath{\metaconstSem{TRACET}}\xspace}
 118
 119 \newcommand*{\relReg}{\metaconstSem{Rel}}
 120 \newcommand*{\relI}[1]{\left[#1\right]}
 121 \newcommand*{\relIP}{\relI{\place}}
 122 \newcommand*{\REL}{\ensuremath{\metaconstSem{REL}}\xspace}
 123 \newcommand*{\RELT}{\ensuremath{\metaconstSem{RELT}}\xspace}
 124 %\DeclareMetaconstSem{\ResultsForAll}{ResultsForAll}
 125 %\DeclareMetaconstSem{\AcceptsForAll}{AcceptsForAll}
 126 \DeclareMetaconstSem{\SIMPLE}{SIMPLE}
 127 \DeclareMetaconstSem{\SIMPLET}{SIMPLET}
 128 \DeclareMetaconstSem{\Result}{Result}
 129
 130 \DeclareMetaconstSem{\FTAPES}{FTAPES}
 131 \DeclareMetaconstSem{\Accepts}{Accepts}
 132 \DeclareMetaconstSem{\ITAPES}{ITAPES}
 133
 134
 135 % homomorphism:
 136 \DeclareMathOperator{\Ext}{\metaconstSemStyle{Ext}}
 137
 138 % functor:
 139 \DeclareMathOperator{\REG}{\metaconstSemStyle{REG}}
 140 \DeclareMathOperator{\REGT}{\metaconstSemStyle{REGT}}
 141
 142 \DeclareMathOperator{\baTests}{\metaconstSemStyle{tests}}
 143
 144 \newcommand{\standardSr}[1]{\mathbb{#1}}
 145 \newcommand{\bbR}{\standardSr{R}}
 146 \newcommand{\bbN}{\standardSr{N}}
 147 \newcommand{\bbZ}{\standardSr{Z}}
 148 \newcommand{\bbB}{\standardSr{B}}
 149
 150 % syntactic:
 151 \newcommand*{\metaconstSyntStyle}[1]{\textnormal{\textrm{#1}}}
 152 \newcommand*{\metaconstSynt}[1]{\text{\metaconstSyntStyle{#1}}}
 153 \newcommand*{\DeclareMetaconstSynt}[2]{\newcommand*{#1}{\metaconstSynt{#2}}}
 154
 155 \newcommand*{\RExp}{\metaconstSynt{RExp}}
 156 \newcommand*{\MRExp}{\metaconstSynt{MRExp}}
 157 \newcommand*{\NFA}{\metaconstSynt{NFA}}
 158 \newcommand*{\DFA}{\metaconstSynt{DFA}}
 159 \newcommand*{\NPS}{\metaconstSynt{NPS}}
 160 \newcommand*{\DPS}{\metaconstSynt{DPS}}
 161 \DeclareMetaconstSynt{\AExp}{AExp}
 162 \DeclareMetaconstSynt{\SumExp}{SumExp}
 163
 164 \newcommand*{\DeclareSyntOp}[2]{\newcommand*{#1}{\metaconstSyntStyle{#2}}}
 165 % homomorphism:
 166 \DeclareSyntOp{\tExpl}{tExpl}
 167 \newcommand*{\Expl}{\tExpl} % alias
 168 \DeclareSyntOp{\detA}{detA}
 169 \DeclareSyntOp{\minA}{minA}
 170
 171 \newcommand*{\kframe}[1]{\mathcal{#1}}
 172 \newcommand*{\fr}[1]{\kframe{#1}} % shorthand
 173 \newcommand*{\kf}[1]{\kframe{#1}} % shorthand
 174 \newcommand*{\autom}[1]{\kframe{#1}}
 175 \newcommand*{\au}[1]{\autom{#1}}
 176 \newcommand*{\structure}[1]{\mathcal{#1}}
 177 \newcommand*{\stru}[1]{\structure{#1}}
 178 \newcommand*{\sr}[1]{\stru{#1}}
 179 \newcommand*{\ka}[1]{\stru{#1}}
 180 \newcommand*{\ba}[1]{\stru{#1}}
 181 \newcommand*{\mo}[1]{\stru{#1}}
 182
 183 \newcommand*{\kaMat}{\ka M}
 184
 185 \newcommand*{\construStyle}[1]{{\normalfont\textsl{#1}}}
 186 \newcommand*{\DeclareConstru}[2]{\DeclareMathOperator{#1}{\construStyle{#2}}}
 187 \DeclareConstru{\Strs}{Strings}
 188 \newcommand*{\eStr}{\epsilon}
 189
 190 \DeclareMathOperator{\Rels}{\construStyle{Relations}}
 191 \newcommand*{\id}{\iota}
 192
 193 \DeclareMathOperator{\Trs}{\construStyle{Traces}}
 194
 195 %\newcommand*{\Strs}[1]{\StrsName(#1)}
 196 %\newcommand*{\Traces}{\construStyle{Traces}}
 197 %\newcommand*{\Relations}{\construStyle{Relations}}
 198
 199
 200 \newcommand*{\Stru}[1]{(#1)}
 201
 202 \newcommand*{\propStyle}[1]{{\normalfont\textbf{#1}}}
 203 \DeclareMathOperator{\First}{\propStyle{first}}
 204 \DeclareMathOperator{\Last}{\propStyle{last}}
 205 \DeclareMathOperator{\Label}{\propStyle{label}}
 206 \DeclareMathOperator{\Length}{\propStyle{length}}
 207 \newcommand*{\Len}[1]{\Length(#1)}
 208
 209 \newcommand*{\trCo}{\diamond}
 210 \newcommand*{\n}[1]{\Bar{#1}}
 211 \newcommand*{\nP}{\n{\place}}
 212
 213 \newcommand*{\ThStyle}[1]{\mathcal{#1}}
 214 \DeclareMathOperator{\EquaOf}{\ThStyle{E}}
 215 \DeclareMathOperator{\HornOf}{\ThStyle{H}}
 216 \DeclareMathOperator{\ThOf}{Th}
 217 % aliases:
 218 \newcommand*{\EOf}{\EquaOf}
 219 \newcommand*{\HOf}{\HornOf}
 220 %
 221 \newcommand*{\thclassStyle}[1]{{\normalfont\textbf{#1}}}
 222 \newcommand*{\DeclareThclass}[2]{\newcommand*{#1}{\ensuremath{\thclassStyle{#2}}}\xspace}
 223 \DeclareThclass{\Equa}{Equa}
 224 \DeclareThclass{\MoEqua}{MoEqua}
 225 \DeclareThclass{\ConservEqua}{ConsEqua}
 226 \newcommand*{\ConsEqua}{\ConservEqua}  % alias
 227 \DeclareThclass{\Commut}{Comm}
 228 \newcommand*{\Comm}{\Commut} % alias
 229 \DeclareThclass{\Annihil}{Annih}
 230 \newcommand*{\Annih}{\Annihil} % alias
 231 \DeclareThclass{\Monot}{Monot}
 232 \DeclareThclass{\Shifts}{Shifts}
 233 \DeclareThclass{\Horn}{Horn}
 234 \DeclareThclass{\Multitape}{MTape}
 235 \newcommand*{\MTape}{\Multitape} % alias
 236 \DeclareThclass{\MultitapeT}{MTapeT}
 237 \newcommand*{\MTapeT}{\MultitapeT} % alias
 238 \newcommand*{\thclass}[1]{\mathfrak{#1}} % vars
 239 \DeclareThclass{\CommutMonot}{CommMonot}
 240 \newcommand*{\CommMonot}{\CommutMonot} % alias
 241 \DeclareThclass{\PCommutMonot}{PCommMonot}
 242 \newcommand*{\PCommMonot}{\PCommutMonot} % alias
 243
 244 \newcommand*{\Atoms}{\metaconstSynt{Atoms}}
 245 \newcommand*{\gsCo}{\trCo}
 246 \DeclareMathOperator{\GS}{\construStyle{GS}}
 247
 248 % complexities:
 249 \newcommand*{\complexityStyle}[1]{{\normalfont\textsl{#1}}}
 250 \newcommand*{\complexity}[1]{\ensuremath{\complexityStyle{#1}}\xspace}
 251 \newcommand*{\DeclareComplexity}[2]{\newcommand*{#1}{\complexity{#2}}}
 252 \DeclareComplexity{\PSPACE}{PSPACE}
 253
 254 \newcommand*{\kfOpStyle}[1]{\construStyle{#1}}
 255 \newcommand*{\DeclareKFOp}[2]{\DeclareMathOperator{#1}{\kfOpStyle{#2}}}
 256 \DeclareKFOp{\kfProduct}{Product}
 257 \DeclareKFOp{\kfUnion}{Union}
 258 \DeclareKFOp{\kfLink}{Link}
 259 \DeclareKFOp{\kfITape}{ITape}
 260 \DeclareKFOp{\kfFTape}{FTape}
 261 \DeclareKFOp{\kfLetter}{Letter}
 262
 263 \newcommand*{\metaconstSyntElStyle}[1]{{\normalfont\textsc{#1}}}
 264 \newcommand*{\metaconstSyntEl}[1]{\metaconstSyntElStyle{#1}}
 265 \newcommand*{\DeclareMetaconstSyntEl}[2]{\newcommand*{#1}{\metaconstSyntEl{#2}}}
 266 \DeclareMetaconstSyntEl{\Start}{start}
 267 \DeclareMetaconstSyntEl{\Stop}{stop}
 268 \newcommand*{\metaconstSemElStyle}[1]{{\normalfont\textsf{#1}}}
 269 \newcommand*{\metaconstSemEl}[1]{\metaconstSemElStyle{#1}}
 270 \newcommand*{\DeclareMetaconstSemEl}[2]{\newcommand*{#1}{\metaconstSemEl{#2}}}
 271 \DeclareMetaconstSemEl{\False}{false}
 272 \DeclareMetaconstSemEl{\True}{true}
 273
 274 \newcommand*{\mathWord}[1]{\text{\textnormal{#1}}}
 275 \newcommand*{\mword}[1]{\mathWord{#1}} % alias
 276 \newcommand*{\Aut}{\mword{A}}
 277 \newcommand*{\EAutOf}{\EOf^{\Aut}}
 278 \newcommand*{\EAOf}{\EAutOf} % alias
 279 \newcommand*{\HAutOf}{\HOf^{\Aut}}
 280 \newcommand*{\HAOf}{\HAutOf} % alias
 281 \newcommand*{\comm}{\mword{c}}
 282 \newcommand*{\Ecomm}{E_{\comm}}
 283 \newcommand*{\pcomm}{\mword{pc}}
 284 \newcommand*{\Epcomm}{E_{\pcomm}}
 285 \newcommand*{\monoid}{\mword{monoid}}
 286 \newcommand*{\Emonoid}{E_{\monoid}}
 287 \newcommand*{\shifts}{\mword{s}}
 288 \newcommand*{\Esh}{E_{\shifts}}
 289 \newcommand*{\mt}{\mword{mt}}
 290 \newcommand*{\Emt}{E_{\mt}}
 291 \newcommand*{\monot}{\mword{m}}
 292 \newcommand*{\Emonot}{E_{\monot}}
 293 \newcommand*{\commmonot}{\mword{cm}}
 294 \newcommand*{\Ecommmonot}{E_{\commmonot}}
 295
 296 \newcommand*{\Indep}{\mathscr I}
 297 \newcommand*{\IndepBy}[1]{\Indep^{#1}}
 298 \newcommand*{\Dep}{\mathscr D}
 299 \newcommand*{\ShiftOf}{\mathscr Q}
 300 \newcommand*{\ShiftBy}[1]{\ShiftOf^{#1}}
 301
 302 \newcommand*{\prStyle}[1]{\text{\textnormal{#1}}}
 303 \newcommand*{\DeclarePr}[2]{\newcommand*{#1}{\prStyle{#2}}}
 304 \DeclarePr{\prINT}{INT}
 305 \DeclarePr{\prINC}{INC}
 306 \DeclarePr{\prEQU}{EQU}
 307 \DeclarePr{\prUNI}{UNI}
 308 \DeclarePr{\prCOM}{COM}
 309 \DeclarePr{\prREC}{REC}
 310
 311 \DeclareConstru{\Frames}{Frames}
 312 \DeclareConstru{\LFrames}{LFrames}
 313 \DeclareConstru{\ILFrames}{ILFrames}
 314 \newcommand*{\coLe}{\sqsubseteq}
 315 \newcommand*{\frCo}{\gsCo}
 316
 317 \newcommand*{\ops}{\mword{ops}}
 318 \newcommand*{\tests}{\mword{tests}}
 319
 320 \newcommand*{\transition}[1]{\xrightarrow{#1}}
 321 \newcommand*{\Entry}[1]{\bullet \transition{#1}}
 322 \newcommand*{\Exit}[1]{\transition{#1} \bullet}
 323
 324 \newcommand*{\preS}{{}_{\sr S}\!}
 325 \newcommand*{\series}[1]{\langle\langle #1 \rangle\rangle}%
 326 \newcommand*{\sums}[1]{\langle #1 \rangle}%
 327 \newcommand*{\reg}{\mword{reg}}
 328
 329 %\usepackage{verbatim}
 330
 331 \newcommand*{\map}{\colon}
 332
 333 \newcommand{\Qm}[1]{\overset{\textbf{?}}{#1}}
 334 \newcommand{\Over}[2]{\underset{\text{ÎÁÄ~#1}}{#2}}
 335
 336 \DeclareMathOperator{\gs}{gs}
 337
 338 %%% Local Variables:
 339 %%% mode: latex
 340 %%% TeX-master: "main"
 341 %%% End: