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strings_and_languages [2009/04/28 20:38] vkuncak |
strings_and_languages [2009/04/28 20:39] vkuncak |
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| \end{eqnarray*} | \end{eqnarray*} | ||
| Therefore, $(\Sigma^*, {\ \cdot\ }, \epsilon)$ is a [[monoid]]. | Therefore, $(\Sigma^*, {\ \cdot\ }, \epsilon)$ is a [[monoid]]. | ||
| - | |||
| - | We sometimes omit $\cdot$ and write $w_1 \cdot w_2$ simply as $w_1 w_2$. | ||
| If $w$ is a word, we define $w^0 = \epsilon$ and $w^{n+1} = w \cdot w^n$. | If $w$ is a word, we define $w^0 = \epsilon$ and $w^{n+1} = w \cdot w^n$. | ||