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A doubt with question:

What is the grammar that generates the language quoted in the description? $$a^nb^{n+m}c^m\text{ for }n≥0, m≥0$$

I don't understand this.

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    $\begingroup$ Do you know what a grammar is, and what a language is ? $\endgroup$ – Denis Sep 10 '13 at 23:58
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The goal is to find a grammar with rules that generate all the words of the form you describe, one example of theses words is $aabbbbbccc$ for $n=2$ and $m=5$.

The following grammar works, with initial symbol $S$ and variables $A,B$:

$\begin{array}{l} S\to AB\\ A\to aAb\\ A\to\epsilon\\ B\to bBc\\ B\to\epsilon \end{array}$

Where $\epsilon$ is the empty word.

For instance to obtain the word above, you can do $S\to AB\to aAbB\to aaAbbB\to aabbB\to aabbbCc\to aabbbbCcc \to aabbbbbCccc \to aabbbbbccc$.

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