1) Show that the following grammar is not LR(0):
           List  -- > Id [ EList ]
           EList -- > Id
           EList -- > EList , Id
 
    ********** SOLUTION **********
    An LR(0) grammar must be able to revert from an input
    string to the starting symbol by parsing what are known as
    handles. A handle is essentially a number of consectutive
    symbols (terminal and non terminal) in the input string.
    
    Given :
        Id [ Id ]
    the longest handle that matches a right hand side
    production is Id.  so the string is converted to:
        Elist [ Id ]
    the next handle is the Id is that is reduced to
        Elist [ Elist ]   
    now there are no more possible conversions, and this is not
    the starting symbol, so the parse failed for a valid string.
 
    The above grammar is not LR(0).
 
 
 8) Consider an item of the form E -- > E * + T.  List five strings
    to which this item might apply and indicate which part of the
    string has been read and which part is still expected to read.
 
    ********** SOLUTION **********
       Input   | have read | left to read    
    ===========*===========*==============
     5 + 2     | 5         | + 2
     3 * 4 + 7 | 3 * 4     | + 7
     6 + 9 * 8 | 6         | + 9 * 8
     1 + 1 + 5 | 1 + 1     | + 1
     5 * 4 + 6 | 5 * 4     | + 6
 
 
 11) Consider the grammar:
           1)  S -- > X X
           2)  X -- > x X
           3)  X -- > y
     
     a) Create the LR(0) items and an SLR(1) parsing table
     b) Using the table created in part (a), parse the string y x x y
 
 
     ********** SOLUTION **********
     Let the asterisk (*) be the position marker:
 
        State 0           State 1
     =============     =============
      S' -- > *S         S' --> S*
      S  -- > *X X
      X  -- > *x X
      X  -- > *y
 
        State 2            State 3
     =============     =============
      S -- > X *X         S --> X X*
      X -- > *x X         
      X -- > *y           
 
        State 4           State 5   
     =============     =============
      X -- > x *X        X --> x X* 
      X -- > *x X  
      X -- > *y           
 
        State 6
     =============
      X -- > y*
 
       State |   x     y     $     |     S     X
      =======*=====================*====================
         0   |  S4    S6           |     1     2 
         1   |              accept |
         2   |  S4    S6           |           3
         3   |              R1     |
         4   |  S4    S6           |           5
         5   |  R2    R2    R2     |           
         6   |  R3    R3    R3     |        
 
 
         Stack		 Input              Action
     =============     =============      ============
     $0                yxxy$               S6
     $0y6              xxy$                R3
     $0X2              xxy$                S4
     $0X2x4            xy$                 S4
     $0X2x4x4          y$                  S6
     $0X2x4x4y6        $                   R3
     $0X2x4x4X5        $                   R2
     $0X2x4X5          $                   R2
     $0X2X3            $                   R1
     $0S1              $                   accept