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Martin Thoma 2014-03-09 16:38:27 +01:00
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documents/Programmierparadigmen/Symbolverzeichnis.tex
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@ -10,11 +10,25 @@ $\emptyset\;\;\;$ Leere Menge\\
$\epsilon\;\;\;$ Das leere Wort\\
$\alpha, \beta\;\;\;$ Reguläre Ausdrücke\\
$L(\alpha)\;\;\;$ Die durch $\alpha$ beschriebene Sprache\\
$L(\alpha | \beta) = L(\alpha) \cup L(\beta)$\\
$L(\alpha \cdot \beta) = L(\alpha) \cdot L(\beta)$\\
$\alpha^+ = L(\alpha)^+$ TODO: Was ist $L(\alpha)^+$\\
$\alpha^* = L(\alpha)^*$ TODO: Was ist $L(\alpha)^*$\\
$\begin{aligned}[t]
L(\alpha | \beta) &= L(\alpha) \cup L(\beta)\\
L(\alpha \cdot \beta)&= L(\alpha) \cdot L(\beta)
\end{aligned}$\\
$L^0 := \Set{\varepsilon}\;\;\;$ Die leere Sprache\\
$L^{n+1} := L^n \circ L \text{ für } n \in \mdn_0\;\;\;$ Potenz einer Sprache\\
$\begin{aligned}[t]
\alpha^+ &=& L(\alpha)^+ &=& \bigcup_{i \in \mdn} L(\alpha)^i\\
\alpha^* &=& L(\alpha)^* &=& \bigcup_{i \in \mdn_0} L(\alpha)^i
\end{aligned}$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Reguläre Ausdrücke %
% Logik %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Logik}
$\mathcal{M} \models \varphi\;\;\;$ Im Modell $\mathcal{M}$ gilt das Prädikat $\varphi$.\\
$\psi \vdash \varphi\;\;\;$ Die Formel $\varphi$ kann aus der Menge der Formeln $\psi$ hergeleitet werden.\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Weiteres %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Weiteres}
$\bot\;\;\;$ Bottom\\