Edit this page Backlinks This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong. ====== Closure properties ====== 1. Show that $(10 \cup 0)^*(1 \cup \epsilon)$ and $(1 \cup \epsilon)(00^*1)^*0^*$ are equivalent regular expressions. 2. Write the "complement" regular expression for $(10 \cup 0)^*(1 \cup \epsilon)$. 3. Define the reversal of a language $L$ as $ rev(L) = \{ w \in \sigma^* | rev(w) \in L \}$, where $rev(c_1c_2..c_n) = c_nc_(n - 1)..c_1$, $c_i \in \sigma, 1 \leq i \leq n$. Show that reversal is a closure property. 4. Let $L \subset \sigma^*$ be a language and $c \in \sigma$ a symbol. The quotient of $L$ and $c$ is the language defined as $L/c = { w \in \sigma^* | wc \in L}$