Mixing
If a language and its complement are context-free, is it regular?
$begingroup$
If both $L$ and $overline{L}$ are context-free, is $L$ necessarily regular?
automata regular-language context-free-grammar
edited Jan 16 at 21:11
Yuval Filmus
48.7k471145
asked Jan 16 at 20:56
Maor RockyMaor Rocky
1348
$endgroup$
add a comment |
$begingroup$
If both $L$ and $overline{L}$ are context-free, is $L$ necessarily regular?
automata regular-language context-free-grammar
edited Jan 16 at 21:11
Yuval Filmus
48.7k471145
asked Jan 16 at 20:56
Maor RockyMaor Rocky
1348
$endgroup$
add a comment |
$begingroup$
If both $L$ and $overline{L}$ are context-free, is $L$ necessarily regular?
automata regular-language context-free-grammar
edited Jan 16 at 21:11
Yuval Filmus
48.7k471145
asked Jan 16 at 20:56
Maor RockyMaor Rocky
1348
$endgroup$
If both $L$ and $overline{L}$ are context-free, is $L$ necessarily regular?
automata regular-language context-free-grammar
automata regular-language context-free-grammar
edited Jan 16 at 21:11
Yuval Filmus
48.7k471145
asked Jan 16 at 20:56
Maor RockyMaor Rocky
1348
edited Jan 16 at 21:11
Yuval Filmus
48.7k471145
asked Jan 16 at 20:56
Maor RockyMaor Rocky
1348
edited Jan 16 at 21:11
Yuval Filmus
48.7k471145
edited Jan 16 at 21:11
Yuval Filmus
48.7k471145
edited Jan 16 at 21:11
Yuval Filmus
48.7k471145
48.7k471145
asked Jan 16 at 20:56
Maor RockyMaor Rocky
1348
asked Jan 16 at 20:56
Maor RockyMaor Rocky
1348
asked Jan 16 at 20:56
Maor RockyMaor Rocky
1348
1348
add a comment |
add a comment |
1 Answer
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$begingroup$
Every deterministic context-free language satisfies this, since the deterministic context-free languages are closed under complementation. Not all deterministic context-free languages are regular, for example ${ a^n b^n : n geq 0 }$ isn't.
answered Jan 16 at 21:11
Yuval FilmusYuval Filmus
48.7k471145
$endgroup$
add a comment |
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$begingroup$
Every deterministic context-free language satisfies this, since the deterministic context-free languages are closed under complementation. Not all deterministic context-free languages are regular, for example ${ a^n b^n : n geq 0 }$ isn't.
answered Jan 16 at 21:11
Yuval FilmusYuval Filmus
48.7k471145
$endgroup$
add a comment |
$begingroup$
Every deterministic context-free language satisfies this, since the deterministic context-free languages are closed under complementation. Not all deterministic context-free languages are regular, for example ${ a^n b^n : n geq 0 }$ isn't.
answered Jan 16 at 21:11
Yuval FilmusYuval Filmus
48.7k471145
$endgroup$
add a comment |
$begingroup$
Every deterministic context-free language satisfies this, since the deterministic context-free languages are closed under complementation. Not all deterministic context-free languages are regular, for example ${ a^n b^n : n geq 0 }$ isn't.
answered Jan 16 at 21:11
Yuval FilmusYuval Filmus
48.7k471145
$endgroup$
Every deterministic context-free language satisfies this, since the deterministic context-free languages are closed under complementation. Not all deterministic context-free languages are regular, for example ${ a^n b^n : n geq 0 }$ isn't.
answered Jan 16 at 21:11
Yuval FilmusYuval Filmus
48.7k471145
answered Jan 16 at 21:11
Yuval FilmusYuval Filmus
48.7k471145
answered Jan 16 at 21:11
Yuval FilmusYuval Filmus
48.7k471145
answered Jan 16 at 21:11
Yuval FilmusYuval Filmus
48.7k471145
48.7k471145
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