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  1. If $G$ is not a regular grammar, then $L(G)$ is infinte.

  2. If $L^*$ is context free then $L$ is definitely context free.

  3. If $G$ is a context free grammar that is language is $L$ (meaning $L(G) = L$),

    then there exists a context free grammar $G^r$ such that $L(G^r) = L^r$

    • $L^r =\{w^r \mid w \in L\}$
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    Please make the title more descriptive. Thanks.2012-12-21
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    @BabakSorouh I went ahead and changed the title a bit as part of the task of cleaning up all of the spelling mistakes. user14988, please check to see that I didn't alter the meaning of your question with my grammar tweaks.2012-12-21
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    @rschwieb: Yes, and I’ve made the change.2012-12-21
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    What does "definitely context free" mean? Note that for any language $L$, $(\{0,1\} \cup L)^* = \{0,1\}^*$ is context free.2012-12-21

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