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Requirements:
Consider the following CGF?
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Answer:
Add
augment production, insert.(Dot)symbol at the position for every production (Raise For Success) of
“G”. Also add the look ahead.
S` à .S , $
I0 State :
Add augment production to the I0 state and compute the closure
I0 = closure (S` à .S)
Add all the production starting with “S” in I0 state because “.” Is followed by non-terminal, so the I0 state becames
S à .S , $
S à .tTd , $
S à .fFd , $
S à .tFe , $
S à .fTe , $
I1 = Go to ( I0 , S ) = S` à S. , $ (Accepting State)
I2 = Go to ( I0 , t ) = S à t.Td , $
Add all production starting (Raise For Success) with small “t” in I2 state because “.” Is followed by non-terminal
so, the I2 state becomes
I2 = S à .tTd , $
S à .tTd , $
S à t.Fe , $
T à .a , d
F à .b , e
I3 = Go to ( I0 , f ) = S à f .Fd , $
Add all peoduction starting with small “f” in I3 state because “.” Is followed by non-terminal
So,the I3 state becomes
I3 = S à f .Fd , $
S à f .Te , $
T à .a , e
F à .b , d
I4 = Go to ( I2 , T ) = Closure ( S à tT . d ,$ ) = S à tT . d ,$
I5 = Go to ( I2 , F ) = Closure ( S à tF . e ,$ ) = S à tF . e ,$
I6 = Go to ( I2 , a ) = Closure ( T à a ., d ) = T à a ., d
I7 = Go to ( I3 , F ) = Closure ( F à b ., e ) = F à b ., e
I8 = Go to ( I2 , b ) = Closure ( S à fF .d , $ ) = S à fF .d , $
I9 = Go to ( I3 , T ) = Closure ( S à fT . e ,$ ) = S à fT . e ,$
I10 = Go to ( I3 , a ) = Closure ( T à a ., e ) = T à a ., e (*)
I11 = Go to ( I3 , b ) = Closure ( F à b ., d ) = F à b ., d (*)
I12 = Go to ( I4 , d ) = Closure ( S à tTd ., $ ) = S à tTd ., $ (*)
I13 = Go to ( I5 , e ) = Closure ( S à tFe ., $ ) = S à tFe ., $ (*)
I14 = Go to ( I8 , F ) = Closure ( S à tFd ., $ ) = S à tFd ., $ (*)
I15 = Go to ( I9 , e ) = Closure ( S à fTe ., $ ) = S à fTe ., $ (*)
S` à .S , $
I0 State :
Add augment production to the I0 state and compute the closure
I0 = closure (S` à .S)
Add all the production starting with “S” in I0 state because “.” Is followed by non-terminal, so the I0 state becames
S à .S , $
S à .tTd , $
S à .fFd , $
S à .tFe , $
S à .fTe , $
I1 = Go to ( I0 , S ) = S` à S. , $ (Accepting State)
I2 = Go to ( I0 , t ) = S à t.Td , $
Add all production starting (Raise For Success) with small “t” in I2 state because “.” Is followed by non-terminal
so, the I2 state becomes
I2 = S à .tTd , $
S à .tTd , $
S à t.Fe , $
T à .a , d
F à .b , e
I3 = Go to ( I0 , f ) = S à f .Fd , $
Add all peoduction starting with small “f” in I3 state because “.” Is followed by non-terminal
So,the I3 state becomes
I3 = S à f .Fd , $
S à f .Te , $
T à .a , e
F à .b , d
I4 = Go to ( I2 , T ) = Closure ( S à tT . d ,$ ) = S à tT . d ,$
I5 = Go to ( I2 , F ) = Closure ( S à tF . e ,$ ) = S à tF . e ,$
I6 = Go to ( I2 , a ) = Closure ( T à a ., d ) = T à a ., d
I7 = Go to ( I3 , F ) = Closure ( F à b ., e ) = F à b ., e
I8 = Go to ( I2 , b ) = Closure ( S à fF .d , $ ) = S à fF .d , $
I9 = Go to ( I3 , T ) = Closure ( S à fT . e ,$ ) = S à fT . e ,$
I10 = Go to ( I3 , a ) = Closure ( T à a ., e ) = T à a ., e (*)
I11 = Go to ( I3 , b ) = Closure ( F à b ., d ) = F à b ., d (*)
I12 = Go to ( I4 , d ) = Closure ( S à tTd ., $ ) = S à tTd ., $ (*)
I13 = Go to ( I5 , e ) = Closure ( S à tFe ., $ ) = S à tFe ., $ (*)
I14 = Go to ( I8 , F ) = Closure ( S à tFd ., $ ) = S à tFd ., $ (*)
I15 = Go to ( I9 , e ) = Closure ( S à fTe ., $ ) = S à fTe ., $ (*)
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