Mixing
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Difference of a regular language and a context-free language
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I know that given the context-free language L and the regular language R, the language L R is context free. But what about R L ? My attempt is as follows:
R L = R $cap$ $overline{L}$
We cannot know whether $overline{L}$ is CF or not, so my guess is that we decide whether R L is context-free or not.
Am I right? Any help would be appreciated.
formal-languages regular-language context-free-grammar
asked Apr 23 '16 at 22:35
SuccessSuccess
967
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add a comment |
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I know that given the context-free language L and the regular language R, the language L R is context free. But what about R L ? My attempt is as follows:
R L = R $cap$ $overline{L}$
We cannot know whether $overline{L}$ is CF or not, so my guess is that we decide whether R L is context-free or not.
Am I right? Any help would be appreciated.
formal-languages regular-language context-free-grammar
asked Apr 23 '16 at 22:35
SuccessSuccess
967
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Well, there is one regular language $R$ of all possible words. So $Rsetminus L=overline{L}$. So if you know of CF languages $L$ so that $overline{L}$ is not CF, then you are done.
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– Thomas Andrews
Apr 23 '16 at 22:39
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@ThomasAndrews Well, I am not given a particular L, so I cannot say anyhting about $overline{L}$ . Am I correct in understanding your comment?
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– Success
Apr 23 '16 at 22:47
add a comment |
$begingroup$
I know that given the context-free language L and the regular language R, the language L R is context free. But what about R L ? My attempt is as follows:
R L = R $cap$ $overline{L}$
We cannot know whether $overline{L}$ is CF or not, so my guess is that we decide whether R L is context-free or not.
Am I right? Any help would be appreciated.
formal-languages regular-language context-free-grammar
asked Apr 23 '16 at 22:35
SuccessSuccess
967
$endgroup$
I know that given the context-free language L and the regular language R, the language L R is context free. But what about R L ? My attempt is as follows:
R L = R $cap$ $overline{L}$
We cannot know whether $overline{L}$ is CF or not, so my guess is that we decide whether R L is context-free or not.
Am I right? Any help would be appreciated.
formal-languages regular-language context-free-grammar
formal-languages regular-language context-free-grammar
asked Apr 23 '16 at 22:35
SuccessSuccess
967
asked Apr 23 '16 at 22:35
SuccessSuccess
967
asked Apr 23 '16 at 22:35
SuccessSuccess
967
asked Apr 23 '16 at 22:35
SuccessSuccess
967
asked Apr 23 '16 at 22:35
SuccessSuccess
967
967
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Well, there is one regular language $R$ of all possible words. So $Rsetminus L=overline{L}$. So if you know of CF languages $L$ so that $overline{L}$ is not CF, then you are done.
$endgroup$
– Thomas Andrews
Apr 23 '16 at 22:39
$begingroup$
@ThomasAndrews Well, I am not given a particular L, so I cannot say anyhting about $overline{L}$ . Am I correct in understanding your comment?
$endgroup$
– Success
Apr 23 '16 at 22:47
add a comment |
$begingroup$
Well, there is one regular language $R$ of all possible words. So $Rsetminus L=overline{L}$. So if you know of CF languages $L$ so that $overline{L}$ is not CF, then you are done.
$endgroup$
– Thomas Andrews
Apr 23 '16 at 22:39
$begingroup$
@ThomasAndrews Well, I am not given a particular L, so I cannot say anyhting about $overline{L}$ . Am I correct in understanding your comment?
$endgroup$
– Success
Apr 23 '16 at 22:47
$begingroup$
Well, there is one regular language $R$ of all possible words. So $Rsetminus L=overline{L}$. So if you know of CF languages $L$ so that $overline{L}$ is not CF, then you are done.
$endgroup$
– Thomas Andrews
Apr 23 '16 at 22:39
$begingroup$
Well, there is one regular language $R$ of all possible words. So $Rsetminus L=overline{L}$. So if you know of CF languages $L$ so that $overline{L}$ is not CF, then you are done.
$endgroup$
– Thomas Andrews
Apr 23 '16 at 22:39
$begingroup$
@ThomasAndrews Well, I am not given a particular L, so I cannot say anyhting about $overline{L}$ . Am I correct in understanding your comment?
$endgroup$
– Success
Apr 23 '16 at 22:47
$begingroup$
@ThomasAndrews Well, I am not given a particular L, so I cannot say anyhting about $overline{L}$ . Am I correct in understanding your comment?
$endgroup$
– Success
Apr 23 '16 at 22:47
add a comment |
1 Answer
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HINT:
Since, regular languages are closed under complement property and context-free languages are not closed under complement property.
answered May 20 '16 at 14:12
Mithlesh UpadhyayMithlesh Upadhyay
2,93282968
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$begingroup$
HINT:
Since, regular languages are closed under complement property and context-free languages are not closed under complement property.
answered May 20 '16 at 14:12
Mithlesh UpadhyayMithlesh Upadhyay
2,93282968
$endgroup$
add a comment |
$begingroup$
HINT:
Since, regular languages are closed under complement property and context-free languages are not closed under complement property.
answered May 20 '16 at 14:12
Mithlesh UpadhyayMithlesh Upadhyay
2,93282968
$endgroup$
add a comment |
$begingroup$
HINT:
Since, regular languages are closed under complement property and context-free languages are not closed under complement property.
answered May 20 '16 at 14:12
Mithlesh UpadhyayMithlesh Upadhyay
2,93282968
$endgroup$
HINT:
Since, regular languages are closed under complement property and context-free languages are not closed under complement property.
answered May 20 '16 at 14:12
Mithlesh UpadhyayMithlesh Upadhyay
2,93282968
answered May 20 '16 at 14:12
Mithlesh UpadhyayMithlesh Upadhyay
2,93282968
answered May 20 '16 at 14:12
Mithlesh UpadhyayMithlesh Upadhyay
2,93282968
answered May 20 '16 at 14:12
Mithlesh UpadhyayMithlesh Upadhyay
2,93282968
2,93282968
add a comment |
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Well, there is one regular language $R$ of all possible words. So $Rsetminus L=overline{L}$. So if you know of CF languages $L$ so that $overline{L}$ is not CF, then you are done.
$endgroup$
– Thomas Andrews
Apr 23 '16 at 22:39
$begingroup$
@ThomasAndrews Well, I am not given a particular L, so I cannot say anyhting about $overline{L}$ . Am I correct in understanding your comment?
$endgroup$
– Success
Apr 23 '16 at 22:47