Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Consider the alphabet∑ ={0,1} , the nul...
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Consider the alphabet ∑ = {0,1} , the null/empty string λ and the set of strings X0,X1 and X2 generated by the corresponding non-terminals of a regular grammar. X0,X1 and X2 are related as follows.
Which one of the following choices precisely represents the strings in X0?
- a)10(0*+(10)*)1
- b)10(0*+(10)*)*1
- c)1(0+10)*1
- d)10(0+10)*1 +110(0+10)*1
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Consider the alphabet∑ ={0,1} , the null/empty stringλ and ...
Here we have little different version of Arden's Theorem
if we have R= PR + Q then it has a solution R = P*Q
Proof : R= PR+ Q
= P(PR+Q)+Q (by putting R= PR+Q)
= P(PR+Q)+Q (by putting R= PR+Q)
= PPR+PQ+Q
=PP(PR+Q)+PQ+Q (by putting R= PR+Q)
= PPPR+PPQ+PQ+Q
and so on , we get R
= {..........+PPPPQ+PPPQ+PPQ+PQ+Q} = {..........+PPPP+PPP+PP+P+ ^}Q = P*Q
or Another way R=PR+Q
= P(P*Q) + Q (by putting R = P*Q)
=(PP* + ^)Q = P*Q
So Equation is Proved .
Now for the Above Question
X1= 0X1 + 1 X2 (Equation 2)
= 0X1 +1(0X1 + ^) ( Put the value of X2 from Equation 3 )
=0X1 +10 X1+ 1 = (0+10)X1 +1
X1= (0+10)*1 (Apply if R = PR + Q then R = P*Q)
X0 = 1 X1 ( Equation 1)
X0 = 1(0+10)*1 ( Put the value of X1 we calculated).
So 1(0+10)*1 option C is correct.
So 1(0+10)*1 option C is correct.
Most Upvoted Answer
Consider the alphabet∑ ={0,1} , the null/empty stringλ and ...
Here we have little different version of Arden's Theorem
if we have R= PR + Q then it has a solution R = P*Q
Proof : R= PR+ Q
= P(PR+Q)+Q (by putting R= PR+Q)
= P(PR+Q)+Q (by putting R= PR+Q)
= PPR+PQ+Q
=PP(PR+Q)+PQ+Q (by putting R= PR+Q)
= PPPR+PPQ+PQ+Q
and so on , we get R
= {..........+PPPPQ+PPPQ+PPQ+PQ+Q} = {..........+PPPP+PPP+PP+P+ ^}Q = P*Q
or Another way R=PR+Q
= P(P*Q) + Q (by putting R = P*Q)
=(PP* + ^)Q = P*Q
So Equation is Proved .
Now for the Above Question
X1= 0X1 + 1 X2 (Equation 2)
= 0X1 +1(0X1 + ^) ( Put the value of X2 from Equation 3 )
=0X1 +10 X1+ 1 = (0+10)X1 +1
X1= (0+10)*1 (Apply if R = PR + Q then R = P*Q)
X0 = 1 X1 ( Equation 1)
X0 = 1(0+10)*1 ( Put the value of X1 we calculated).
So 1(0+10)*1 option C is correct.
So 1(0+10)*1 option C is correct.
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Community Answer
Consider the alphabet∑ ={0,1} , the null/empty stringλ and ...
Here we have little different version of Arden's Theorem
if we have R= PR + Q then it has a solution R = P*Q
Proof : R= PR+ Q
= P(PR+Q)+Q (by putting R= PR+Q)
= P(PR+Q)+Q (by putting R= PR+Q)
= PPR+PQ+Q
=PP(PR+Q)+PQ+Q (by putting R= PR+Q)
= PPPR+PPQ+PQ+Q
and so on , we get R
= {..........+PPPPQ+PPPQ+PPQ+PQ+Q} = {..........+PPPP+PPP+PP+P+ ^}Q = P*Q
or Another way R=PR+Q
= P(P*Q) + Q (by putting R = P*Q)
=(PP* + ^)Q = P*Q
So Equation is Proved .
Now for the Above Question
X1= 0X1 + 1 X2 (Equation 2)
= 0X1 +1(0X1 + ^) ( Put the value of X2 from Equation 3 )
=0X1 +10 X1+ 1 = (0+10)X1 +1
X1= (0+10)*1 (Apply if R = PR + Q then R = P*Q)
X0 = 1 X1 ( Equation 1)
X0 = 1(0+10)*1 ( Put the value of X1 we calculated).
So 1(0+10)*1 option C is correct.
So 1(0+10)*1 option C is correct.
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Consider the alphabet∑ ={0,1} , the null/empty stringλ and the set of strings X0,X1 and X2 generated by the corresponding non-terminals of a regular grammar. X0,X1 and X2are related as follows.Which one of the following choices precisely represents the strings in X0?a)10(0*+(10)*)1b)10(0*+(10)*)*1c)1(0+10)*1d)10(0+10)*1 +110(0+10)*1Correct answer is option 'C'. Can you explain this answer?
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