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strings_and_languages [2012/09/19 16:56] vkuncak |
strings_and_languages [2019/07/02 16:16] fabien [Strings and languages] |
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| Observe that | Observe that | ||
| - | \[ | + | \begin{equation*} |
| \emptyset \cdot L = \{ s_1 \cdot s_2 \mid s_1 \in \emptyset \land s_2 \in L \} = \{s_1 \cdot s_2 \mid \mbox{false} \} = \emptyset | \emptyset \cdot L = \{ s_1 \cdot s_2 \mid s_1 \in \emptyset \land s_2 \in L \} = \{s_1 \cdot s_2 \mid \mbox{false} \} = \emptyset | ||
| - | \] | + | \end{equation*} |
| Similarly, $L \cdot \emptyset = \emptyset$. | Similarly, $L \cdot \emptyset = \emptyset$. | ||
| Also directly from definition follows: | Also directly from definition follows: | ||
| - | \[ | + | \begin{equation*} |
| \{ w_1 \} \cdot \{ w_2 \} = \{ w_1\cdot w_2 \} | \{ w_1 \} \cdot \{ w_2 \} = \{ w_1\cdot w_2 \} | ||
| - | \] | + | \end{equation*} |