From 97cdff91726001fb87e6d8c0f3bf0bdd8fc75699 Mon Sep 17 00:00:00 2001
From: Gregor Kleen <gkleen@yggdrasil.li>
Date: Fri, 22 Apr 2016 20:34:15 +0200
Subject: fsk 00

---
 ss2016/fsk/00/abgabe.md | 23 +++++++++++++++++++++++
 1 file changed, 23 insertions(+)
 create mode 100644 ss2016/fsk/00/abgabe.md

(limited to 'ss2016/fsk')

diff --git a/ss2016/fsk/00/abgabe.md b/ss2016/fsk/00/abgabe.md
new file mode 100644
index 0000000..ded4685
--- /dev/null
+++ b/ss2016/fsk/00/abgabe.md
@@ -0,0 +1,23 @@
+1)
+
+|      $\in$ | $L$    | $L^+$  | $L^\ast$   | $L^\ast\{c\}^+$   |
+|-----------:+:------:+:------:+:----------:+:-----------------:|
+| $\epsilon$ | $\bot$ | $\bot$ | $\top$     | $\bot$            |
+|       $ab$ | $\top$ | $\top$ | $\top$     | $\bot$            |
+|      $abc$ | $\bot$ | $\bot$ | $\bot$     | $\top$            |
+|     $bcab$ | $\bot$ | $\top$ | $\top$     | $\bot$            |
+|   $bcabbc$ | $\bot$ | $\top$ | $\top$     | $\bot$            |
+
+2)
+
+| $\in$    | $R$    | $R^+$  | $R^\ast$ |
+|---------:+:------:+:------:+:--------:|
+| $(3,3)$  | $\bot$ | $\bot$ | $\top$   |
+| $(3,6)$  | $\top$ | $\top$ | $\top$   |
+| $(3,18)$ | $\bot$ | $\bot$ | $\bot$   |
+| $(3,24)$ | $\bot$ | $\top$ | $\top$   |
+
+5)  a)  $\{(S, b), (aS, aaS), (b, ab), (ab, aab\}$
+    b)  $\{(S, b), (S, aaab), (aS, aaaaS), (b, aaab), (b, aaaab), (aab, aaaab)\}$
+    c)  $\{ a^n S^x b^{\lnot x} \mid x \in \{0, 1\} \land n \in \N \}$, wobei $\lnot 0 = 1$ und $\lnot 1 = 0$
+    d)  $L(G) = \{ a^nb \mid n \in \N \}$
-- 
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