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}