%!TEX root = Programmierparadigmen.tex \markboth{Symbolverzeichnis}{Symbolverzeichnis} \chapter*{Symbolverzeichnis} \addcontentsline{toc}{chapter}{Symbolverzeichnis} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Reguläre Ausdrücke % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section*{Reguläre Ausdrücke} $\emptyset\;\;\;$ Leere Menge\\ $\epsilon\;\;\;$ Das leere Wort\\ $\alpha, \beta\;\;\;$ Reguläre Ausdrücke\\ $L(\alpha)\;\;\;$ Die durch $\alpha$ beschriebene Sprache\\ $\begin{aligned}[t] L(\alpha | \beta) &= L(\alpha) \cup L(\beta)\\ L(\alpha \cdot \beta)&= L(\alpha) \cdot L(\beta) \end{aligned}$\\ $L^0 := \Set{\varepsilon}\;\;\;$ Die leere Sprache\\ $L^{n+1} := L^n \circ L \text{ für } n \in \mdn_0\;\;\;$ Potenz einer Sprache\\ $\begin{aligned}[t] \alpha^+ &=& L(\alpha)^+ &=& \bigcup_{i \in \mdn} L(\alpha)^i\\ \alpha^* &=& L(\alpha)^* &=& \bigcup_{i \in \mdn_0} L(\alpha)^i \end{aligned}$ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 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\\