A$)$ Write a recognizer in C$++$ for L $=\{$x $|$ x contains any combination of $0$s and $1$s $\}[33$ points$]$

My recognizer.cpp must be used.

main: Given a string $($from $)$ cined from the user, pass it to

the recognizer function.

Cout $$YES IN L$$ or $$NO NOT IN L$$ depending on what was returned.

recognizer function: Should return TRUE or FALSE checking each character

to make sure it is an $0$ or a $1.$

Testing: test with $0,1,00110,2,02,31$ in this order. $$Routput$.$txt

B$)$ Write a generator in C$++$ for L $=\{$x $|$ x contains any combination of $0$s and $1$s$\}.$

My generator.cpp must be used.

main: It should create each string over E $=\{0,1,2\}$ systematically

$($short to long$)$ and pass each string to the recognizer function

created in Part a$)$ above.

Only those strings for which the recognizer returned TRUE

should be displayed.

for example,

create $0-->$ returns TRUE $--->$ display $0$

create $1-->$ returns TRUE $--->$ display $1$

create $2-->$ returns FALSE

create $00-->$ returns TRUE $--->$ display $00$

create $01-->$ returns TRUE $--->$ display $01$

create $02-->$ returns FALSE

create $10-->$ returns TRUE $--->$ display $10$ and keep on going

create $11-->$ returns TRUE $--->$ display $11$ and keep on going

$[$The challenge here is to figure out how to create

all strings using $0,1$ and $2$ systematically, with no repeated

strings. $]$

recognizer function: the same one from part A$)($copy and use$)$

Testing: The user must somehow interactively terminate

the execution of the program after at least $20$ strings containing $0$s and $1$s have been displayed,

although your program should be able to keep on going until the queue overflows. $$Goutput$.$txt