From b0eec2f64434a8cee24e82f990003a5f473b0639 Mon Sep 17 00:00:00 2001
From: Sheppy <jupiterfisch@web.de>
Date: Wed, 7 Oct 2015 23:39:35 +0200
Subject: [PATCH] PumpingLemma commit cleanup added to makefile

---
 Vorlesungen/ThProg/Makefile         |  5 ++++-
 Vorlesungen/ThProg/PumpingLemma.tex | 19 +++++++++++++++++--
 2 files changed, 21 insertions(+), 3 deletions(-)

diff --git a/Vorlesungen/ThProg/Makefile b/Vorlesungen/ThProg/Makefile
index 503a7fb..88ae73f 100644
--- a/Vorlesungen/ThProg/Makefile
+++ b/Vorlesungen/ThProg/Makefile
@@ -2,10 +2,13 @@ all: Konfluenz.pdf Koinduktion_reduktion.pdf Strukturelle_Induktion.pdf Polynomo
 
 continuous: $(PDF).continuous 
 
+cleanup: 
+	-rm -f *.aux *.fdb_latexmk *.fls *.log
+
 %.continuous: %.pdf
 	latexmk -jobname=$(@:%.continuous=%) -pvc -pdf $(@:%.continuous=%).tex
 
 %.pdf: %.tex
 	latexmk -jobname=$(@:%.pdf=%) -pdf $<
 
-.PHONY: all continuous
+.PHONY: all continuous cleanup
diff --git a/Vorlesungen/ThProg/PumpingLemma.tex b/Vorlesungen/ThProg/PumpingLemma.tex
index acb5f71..b4b1db1 100644
--- a/Vorlesungen/ThProg/PumpingLemma.tex
+++ b/Vorlesungen/ThProg/PumpingLemma.tex
@@ -1,14 +1,29 @@
 	\documentclass{article}
 	\usepackage{amsmath}
+	\usepackage{ amssymb } % >= as \geq
 	\usepackage{nccmath}
+	%New Commands
+	\newcommand{\xhspace}[0]{\noindent\hspace*{5mm}}
 	\DeclareMathSizes{10}{10}{10}{10}
 	\setlength{\parindent}{0pt}
-	\title{Struckturelle Induktion}
+	\title{Pumping Lemme f\"ur Regul\"are Sprachen}
 	\date{ }
 	\begin{document}
 	\maketitle
 	%----------------------------------%
-	
+	\textbf{L ist regul\"ar wenn:}
+		\[		
+			\forall l \geq 1\;.\, \exists w \in L\;mit\; |w|\geq l
+		\]
+	\textbf{sodass:}\\
+		\xhspace	$\forall$ uvz \\
+	\textbf{mit:}\\ 
+		\xhspace	w=uvz\\
+		\xhspace	$|$v$|$ $\geq$ 1\\
+		\xhspace	$|$uv$|$ $\leq$ l\\
+	\textbf{gilt:}\\
+		\xhspace	u$v^{k}$z $\notin$ L 
+
 	\begin{tiny}
 	\copyright\ Joint-Troll-Expert-Group (JTEG) 2015
 	\end{tiny}