Please help in solving this question a veii big doubt

Question

Comments

LEADING(S)={a ^ ( ,}

LEADING(T)={ , }

TRAILING(S)={ a ^ ) , }

TRAILING(T)={ , }

 Am i Right?

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please share the book name for the picture/ques shown above. Also, clarify Leading(T).

Answer 1

Given Grammar = 

S -> a | ^ | ( T )

T -> T , S | S

(b) .

Leading (S) =  Leading ( T ) =  {" a" , " ^"  , "  (  " } 

Trailing ( S) =  Trailing  ( T )  =  {  " )  " ,   " , (comma) "  , "  $  "  }

(c)  Precedence of operators =>

       Assuming here only two operators. 1. ^ 2. ,(comma).

       Precedence of , ( comma ) operator is greater than ^ operator.   

(a)  Given string S = ( ( ( a , a , ^ , (a) ) , a ).

  I think, The given string is not correct. Because,  it does not follow balanced parentheses.

 So, I am assuming it as S = ( ( a , a , ^ , (a) ) , a )

Now, lets see all shift and reduce steps.

  S - > ( T )                                    // shift = > S -> ( T)   

  S  - > ( T , S )                              // shift  = > T - > T , S

  S  ->  ( T , a )                              // reduction => S -> a

  S  - > ( S , a)                               // shift => T -> S

  S  - > ( ( T ) , a)                            / / shift  => S -> ( T )

  S  -> (  T , S )  , a )                       // shift =>  T - > T , S

  S  -> ( ( T , ( T ) ) , a)                     // shift  => S -> ( T )

  S  -> ( ( T , ( S ) ) , a)                     //  shift   => T -> S

  S  -> ( ( T , ( a ) ) , a)                     //reduction => S -> a  

  S  -> ( ( T , S , ( a ) ) , a)                // shift =>  T - > T , S

  S  -> ( ( T , ^ , ( a ) ) , a)                 //reduction => S -> ^

  S  -> ( ( T , S , ^ , ( a ) ) , a)            // shift =>  T - > T , S

  S  -> ( ( T , a , ^ , ( a ) ) , a)             //reduction => S -> a

  S  -> ( ( S , a , ^ , ( a ) ) , a)             //  shift   => T -> S

  S  -> ( ( a , a , ^ , ( a ) ) , a)              // reduction => S -> a

  

Correct me if I am wrong  .. 

Comments

respected  vijaycs sir i dont think you are correct sir.

Part a) correct answer is the answer which i posted as the question says to show the steps for shift reduce parser after each proper shift and reduce action so that string can be accepted By the Shift Reduce parser. 

since the string is accepted hence it is parsed properly by Shift Reduce Parser. 

part c) since it is parsed properly by Shift reduce hence it is Operator precedance grammar also 

just having confusion with part b)

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anybody please clear it ??

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Leading and trailing