Mixing
Regular Grammar
$begingroup$
Devise a regular grammar in normal form that generates the language L.
Let L be the language consisting of all binary numbers
divisible by 4.
I know the different aspects needed to be generated:
starting point, non terminals and production rules etc.
Need help on how to generate though
discrete-mathematics computer-science regular-language context-free-grammar
asked Jan 23 at 20:46
SueSue
126
$endgroup$
add a comment |
$begingroup$
Devise a regular grammar in normal form that generates the language L.
Let L be the language consisting of all binary numbers
divisible by 4.
I know the different aspects needed to be generated:
starting point, non terminals and production rules etc.
Need help on how to generate though
discrete-mathematics computer-science regular-language context-free-grammar
asked Jan 23 at 20:46
SueSue
126
$endgroup$
$begingroup$
hint you need to generate ${1*}00$ strings
$endgroup$
– zwim
Jan 23 at 21:01
$begingroup$
@zwim Would be in form {p w q | p E {1}*, w E{1,0}* , q^n E {0} , n>=2 }
$endgroup$
– Sue
Jan 23 at 21:27
add a comment |
$begingroup$
Devise a regular grammar in normal form that generates the language L.
Let L be the language consisting of all binary numbers
divisible by 4.
I know the different aspects needed to be generated:
starting point, non terminals and production rules etc.
Need help on how to generate though
discrete-mathematics computer-science regular-language context-free-grammar
asked Jan 23 at 20:46
SueSue
126
$endgroup$
Devise a regular grammar in normal form that generates the language L.
Let L be the language consisting of all binary numbers
divisible by 4.
I know the different aspects needed to be generated:
starting point, non terminals and production rules etc.
Need help on how to generate though
discrete-mathematics computer-science regular-language context-free-grammar
discrete-mathematics computer-science regular-language context-free-grammar
asked Jan 23 at 20:46
SueSue
126
asked Jan 23 at 20:46
SueSue
126
asked Jan 23 at 20:46
SueSue
126
asked Jan 23 at 20:46
SueSue
126
asked Jan 23 at 20:46
SueSue
126
126
$begingroup$
hint you need to generate ${1*}00$ strings
$endgroup$
– zwim
Jan 23 at 21:01
$begingroup$
@zwim Would be in form {p w q | p E {1}*, w E{1,0}* , q^n E {0} , n>=2 }
$endgroup$
– Sue
Jan 23 at 21:27
add a comment |
$begingroup$
hint you need to generate ${1*}00$ strings
$endgroup$
– zwim
Jan 23 at 21:01
$begingroup$
@zwim Would be in form {p w q | p E {1}*, w E{1,0}* , q^n E {0} , n>=2 }
$endgroup$
– Sue
Jan 23 at 21:27
$begingroup$
hint you need to generate ${1*}00$ strings
$endgroup$
– zwim
Jan 23 at 21:01
$begingroup$
hint you need to generate ${1*}00$ strings
$endgroup$
– zwim
Jan 23 at 21:01
$begingroup$
@zwim Would be in form {p w q | p E {1}*, w E{1,0}* , q^n E {0} , n>=2 }
$endgroup$
– Sue
Jan 23 at 21:27
$begingroup$
@zwim Would be in form {p w q | p E {1}*, w E{1,0}* , q^n E {0} , n>=2 }
$endgroup$
– Sue
Jan 23 at 21:27
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
A binary string is divisible by 4 if and only if it is $0$ or ends in $00$.
So, you could pretty easily do something like
$$
begin{align*}
S&rightarrow0\
S&rightarrow 1N\
N&rightarrow 0N\
N&rightarrow 0F\
F&rightarrow0
end{align*}
$$
Explanation:
Our underlying alphabet (set of terminals) is ${0,1}$. $S$ is our start, $N$ is a non-terminal representing the part of any such non-zero number that follows the initial $1$, and $F$ is a non-terminal indicating that we've put in the first of our two final $0$'s.
From $S$ you either go straight to $0$ and are done, or you have an initial $1$. Following an initial $1$ is any number of $0$'s and $1$'s, followed by a final $00$.
answered Jan 23 at 22:43
Nick PetersonNick Peterson
26.8k23962
$endgroup$
add a comment |
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1 Answer
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active
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1 Answer
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active
oldest
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votes
$begingroup$
A binary string is divisible by 4 if and only if it is $0$ or ends in $00$.
So, you could pretty easily do something like
$$
begin{align*}
S&rightarrow0\
S&rightarrow 1N\
N&rightarrow 0N\
N&rightarrow 0F\
F&rightarrow0
end{align*}
$$
Explanation:
Our underlying alphabet (set of terminals) is ${0,1}$. $S$ is our start, $N$ is a non-terminal representing the part of any such non-zero number that follows the initial $1$, and $F$ is a non-terminal indicating that we've put in the first of our two final $0$'s.
From $S$ you either go straight to $0$ and are done, or you have an initial $1$. Following an initial $1$ is any number of $0$'s and $1$'s, followed by a final $00$.
answered Jan 23 at 22:43
Nick PetersonNick Peterson
26.8k23962
$endgroup$
add a comment |
$begingroup$
A binary string is divisible by 4 if and only if it is $0$ or ends in $00$.
So, you could pretty easily do something like
$$
begin{align*}
S&rightarrow0\
S&rightarrow 1N\
N&rightarrow 0N\
N&rightarrow 0F\
F&rightarrow0
end{align*}
$$
Explanation:
Our underlying alphabet (set of terminals) is ${0,1}$. $S$ is our start, $N$ is a non-terminal representing the part of any such non-zero number that follows the initial $1$, and $F$ is a non-terminal indicating that we've put in the first of our two final $0$'s.
From $S$ you either go straight to $0$ and are done, or you have an initial $1$. Following an initial $1$ is any number of $0$'s and $1$'s, followed by a final $00$.
answered Jan 23 at 22:43
Nick PetersonNick Peterson
26.8k23962
$endgroup$
add a comment |
$begingroup$
A binary string is divisible by 4 if and only if it is $0$ or ends in $00$.
So, you could pretty easily do something like
$$
begin{align*}
S&rightarrow0\
S&rightarrow 1N\
N&rightarrow 0N\
N&rightarrow 0F\
F&rightarrow0
end{align*}
$$
Explanation:
Our underlying alphabet (set of terminals) is ${0,1}$. $S$ is our start, $N$ is a non-terminal representing the part of any such non-zero number that follows the initial $1$, and $F$ is a non-terminal indicating that we've put in the first of our two final $0$'s.
From $S$ you either go straight to $0$ and are done, or you have an initial $1$. Following an initial $1$ is any number of $0$'s and $1$'s, followed by a final $00$.
answered Jan 23 at 22:43
Nick PetersonNick Peterson
26.8k23962
$endgroup$
A binary string is divisible by 4 if and only if it is $0$ or ends in $00$.
So, you could pretty easily do something like
$$
begin{align*}
S&rightarrow0\
S&rightarrow 1N\
N&rightarrow 0N\
N&rightarrow 0F\
F&rightarrow0
end{align*}
$$
Explanation:
Our underlying alphabet (set of terminals) is ${0,1}$. $S$ is our start, $N$ is a non-terminal representing the part of any such non-zero number that follows the initial $1$, and $F$ is a non-terminal indicating that we've put in the first of our two final $0$'s.
From $S$ you either go straight to $0$ and are done, or you have an initial $1$. Following an initial $1$ is any number of $0$'s and $1$'s, followed by a final $00$.
answered Jan 23 at 22:43
Nick PetersonNick Peterson
26.8k23962
answered Jan 23 at 22:43
Nick PetersonNick Peterson
26.8k23962
answered Jan 23 at 22:43
Nick PetersonNick Peterson
26.8k23962
answered Jan 23 at 22:43
Nick PetersonNick Peterson
26.8k23962
26.8k23962
add a comment |
add a comment |
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$begingroup$
hint you need to generate ${1*}00$ strings
$endgroup$
– zwim
Jan 23 at 21:01
$begingroup$
@zwim Would be in form {p w q | p E {1}*, w E{1,0}* , q^n E {0} , n>=2 }
$endgroup$
– Sue
Jan 23 at 21:27