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    <p>You need them to be able to construct the strings that are in the language <code>L</code>.</p> <p><code>B --&gt; aBb | A</code> means that if you have a nonterminal <code>B</code> it can be replaced by either <code>aBb</code> <em>or</em> <code>A</code>. (Capital letters represent nonterminals and the lower case letters represent terminals).</p> <p>Let's take a look at the grammar:</p> <pre><code>S --&gt; B | ^ B --&gt; aBb | A A --&gt; aA | a </code></pre> <p><strong>Why do we have a <code>| ^</code>?</strong> You need it to be able to generate the empty string. The empty string is clearly part of the language <code>L</code> since it contain an equal amount of <code>a</code>s and <code>b</code>s.</p> <p><strong>Why do we have <code>| A</code>?</strong> To be able to use the rule for <code>A</code>. Now you can replace <code>B</code> with <code>A</code> so you can insert either <code>aA</code> or <code>a</code>. You need this rule to be able to generate strings that have more <code>a</code>s than <code>b</code>s.</p> <p><strong>Why do we have <code>| a</code>?</strong> To be able to replace <code>A</code> with <code>a</code> <em>without</em> adding a new nonterminal that need to be replaced. </p> <p>When I look at this grammar I would say that you need to change <code>A --&gt; aA | a</code> to <code>A --&gt; aA | a | ^</code> to be able to generate strings with an equal amount of <code>a</code>s and <code>b</code>s. (So you can replace <code>A</code> with the empty string (or null) instead of having to add an extra <code>a</code>)</p> <p>Let's say you want to generate the string <code>aaabb</code>:</p> <pre><code>S //You start with S B //Rule: S --&gt; B aBb //Rule: B --&gt; aBb aaBbb //Rule: B --&gt; aBb aaAbb //Rule: B --&gt; A aaabb //Rule: A --&gt; a </code></pre>
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    1. POWhy s--> ^ and A --> a ? in Context Free Grammars
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    1. COBrilliant, thanks! Can you explain what this symbol means: http://d.pr/i/3YG1 - thanks again.
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    2. CO@Xiy That sign is the "not equal" sign. See [this](http://en.wikipedia.org/wiki/Equals_sign#Not_equal)
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    3. COI see. The example provided as really helpful, thank you.
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