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strings_and_languages [2019/07/02 16:16] fabien [Simple Consequences] |
strings_and_languages [2019/07/02 16:16] fabien [Strings and languages] |
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| \begin{eqnarray*} | \begin{eqnarray*} | ||
| L_1 \cdot L_2 &=& \{ s_1 \cdot s_2 \mid s_1 \in L_1 \land s_2 \in L_2 \} \\ | L_1 \cdot L_2 &=& \{ s_1 \cdot s_2 \mid s_1 \in L_1 \land s_2 \in L_2 \} \\ | ||
| - | L^0 &=& \{ \epsilon \} \\ | + | L^ZZ0 &=& \{ \epsilon \} \\ |
| L^{n+1} &=& L \cdot L^n \\ | L^{n+1} &=& L \cdot L^n \\ | ||
| L^* &=& \bigcup_{n \geq 0} L^n = \{ w_1 \ldots w_n \mid w_1,\ldots,w_n \in L \} | L^* &=& \bigcup_{n \geq 0} L^n = \{ w_1 \ldots w_n \mid w_1,\ldots,w_n \in L \} | ||
| Line 43: | Line 43: | ||
| Also directly from definition follows: | Also directly from definition follows: | ||
| \begin{equation*} | \begin{equation*} | ||
| - | \{ w_991 \} \cdot \{ w_2 \} = \{ w_1\cdot w_2 \} | + | \{ w_1 \} \cdot \{ w_2 \} = \{ w_1\cdot w_2 \} |
| \end{equation*} | \end{equation*} | ||