Mixing
Finding languages such that $L_{1} subseteq L_{2} subseteq L_{3}$ where $L_{1}, L_{3} notin mathbb{R}$,...
$begingroup$
I am struggling to find such languages $L_{1}$, $L_{2}$, and $L_{3}$ such that
$$
L_{1} subseteq L_{2} subseteq L_{3}
$$
where $L_{1}, L_{3} notin mathbb{R}$ and $L_{2} in mathbb{R}$.
I know they exist, I need help finding them.
computability formal-languages automata turing-machines
edited Jan 9 at 1:51
amWhy
1
asked Jan 8 at 23:47
Tomer LevyTomer Levy
406
$endgroup$
add a comment |
$begingroup$
I am struggling to find such languages $L_{1}$, $L_{2}$, and $L_{3}$ such that
$$
L_{1} subseteq L_{2} subseteq L_{3}
$$
where $L_{1}, L_{3} notin mathbb{R}$ and $L_{2} in mathbb{R}$.
I know they exist, I need help finding them.
computability formal-languages automata turing-machines
edited Jan 9 at 1:51
amWhy
1
asked Jan 8 at 23:47
Tomer LevyTomer Levy
406
$endgroup$
$begingroup$
What does $Bbb R$ mean here?
$endgroup$
– MJD
Jan 10 at 21:39
add a comment |
$begingroup$
I am struggling to find such languages $L_{1}$, $L_{2}$, and $L_{3}$ such that
$$
L_{1} subseteq L_{2} subseteq L_{3}
$$
where $L_{1}, L_{3} notin mathbb{R}$ and $L_{2} in mathbb{R}$.
I know they exist, I need help finding them.
computability formal-languages automata turing-machines
edited Jan 9 at 1:51
amWhy
1
asked Jan 8 at 23:47
Tomer LevyTomer Levy
406
$endgroup$
I am struggling to find such languages $L_{1}$, $L_{2}$, and $L_{3}$ such that
$$
L_{1} subseteq L_{2} subseteq L_{3}
$$
where $L_{1}, L_{3} notin mathbb{R}$ and $L_{2} in mathbb{R}$.
I know they exist, I need help finding them.
computability formal-languages automata turing-machines
computability formal-languages automata turing-machines
edited Jan 9 at 1:51
amWhy
1
asked Jan 8 at 23:47
Tomer LevyTomer Levy
406
edited Jan 9 at 1:51
amWhy
1
asked Jan 8 at 23:47
Tomer LevyTomer Levy
406
edited Jan 9 at 1:51
amWhy
1
edited Jan 9 at 1:51
amWhy
1
edited Jan 9 at 1:51
amWhy
1
1
asked Jan 8 at 23:47
Tomer LevyTomer Levy
406
asked Jan 8 at 23:47
Tomer LevyTomer Levy
406
asked Jan 8 at 23:47
Tomer LevyTomer Levy
406
406
$begingroup$
What does $Bbb R$ mean here?
$endgroup$
– MJD
Jan 10 at 21:39
add a comment |
$begingroup$
What does $Bbb R$ mean here?
$endgroup$
– MJD
Jan 10 at 21:39
$begingroup$
What does $Bbb R$ mean here?
$endgroup$
– MJD
Jan 10 at 21:39
$begingroup$
What does $Bbb R$ mean here?
$endgroup$
– MJD
Jan 10 at 21:39
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Any language $L$ over a finite alphabet $Sigma$ is both contained in some regular language and in some non-regular language.
Firstly, $Sigma^*$ is regular and contains the language.
Secondly, if $x,ynotinSigma$, then ${sx^ny^n:sin L,ninmathbb{N}}$ is non-regular and contains $L$. The standard proof that ${x^ny^n:ninmathbb{N}}$ is non-regular using the pumping lemma can be copied completely to prove this.
answered Jan 9 at 0:04
SmileyCraftSmileyCraft
3,566517
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add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Any language $L$ over a finite alphabet $Sigma$ is both contained in some regular language and in some non-regular language.
Firstly, $Sigma^*$ is regular and contains the language.
Secondly, if $x,ynotinSigma$, then ${sx^ny^n:sin L,ninmathbb{N}}$ is non-regular and contains $L$. The standard proof that ${x^ny^n:ninmathbb{N}}$ is non-regular using the pumping lemma can be copied completely to prove this.
answered Jan 9 at 0:04
SmileyCraftSmileyCraft
3,566517
$endgroup$
add a comment |
$begingroup$
Any language $L$ over a finite alphabet $Sigma$ is both contained in some regular language and in some non-regular language.
Firstly, $Sigma^*$ is regular and contains the language.
Secondly, if $x,ynotinSigma$, then ${sx^ny^n:sin L,ninmathbb{N}}$ is non-regular and contains $L$. The standard proof that ${x^ny^n:ninmathbb{N}}$ is non-regular using the pumping lemma can be copied completely to prove this.
answered Jan 9 at 0:04
SmileyCraftSmileyCraft
3,566517
$endgroup$
add a comment |
$begingroup$
Any language $L$ over a finite alphabet $Sigma$ is both contained in some regular language and in some non-regular language.
Firstly, $Sigma^*$ is regular and contains the language.
Secondly, if $x,ynotinSigma$, then ${sx^ny^n:sin L,ninmathbb{N}}$ is non-regular and contains $L$. The standard proof that ${x^ny^n:ninmathbb{N}}$ is non-regular using the pumping lemma can be copied completely to prove this.
answered Jan 9 at 0:04
SmileyCraftSmileyCraft
3,566517
$endgroup$
Any language $L$ over a finite alphabet $Sigma$ is both contained in some regular language and in some non-regular language.
Firstly, $Sigma^*$ is regular and contains the language.
Secondly, if $x,ynotinSigma$, then ${sx^ny^n:sin L,ninmathbb{N}}$ is non-regular and contains $L$. The standard proof that ${x^ny^n:ninmathbb{N}}$ is non-regular using the pumping lemma can be copied completely to prove this.
answered Jan 9 at 0:04
SmileyCraftSmileyCraft
3,566517
answered Jan 9 at 0:04
SmileyCraftSmileyCraft
3,566517
answered Jan 9 at 0:04
SmileyCraftSmileyCraft
3,566517
answered Jan 9 at 0:04
SmileyCraftSmileyCraft
3,566517
3,566517
add a comment |
add a comment |
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$begingroup$
What does $Bbb R$ mean here?
$endgroup$
– MJD
Jan 10 at 21:39