1. Consider the following context-free grammar:

               S -> S B
                 -> y
               B -> B x
                 -> A x
               A -> z
                 -> z S y

   a) Show that the grammar is not LL(1).

   b) Modify the grammar so that it becomes LL(1).

   c) Construct the corresponding LL(1) parse table.

   d) Write the skeleton of the corresponding recursive descent parser.



2. Write a context free grammar with the following characteristics:

   a). The language is composed of expressions, with operators and the atomic
       symbol 'a';

   b). The language has the following operator precedence hierarchy:
	_________________________________________________________________
	|Level         | Operator | Type of Op.   | Associability 	|
        _________________________________________________________________
	|Least binding | '*' 	  | Binary Infix  | 	Left 		|
  	|	       | '+'	  | Binary Infix  | 	Right		|
  	|	       | '#' 	  | Unary Prefix  | 	None		|
  	|	       | '~' 	  | Unary Postfix | 	None		|
	|Most binding  |'(' ')'   | Embedding 	  |	None		|
        __________________________________________________________________

    c) Show the derivation tree and the abstract syntax tree for the following
       expression:

	a * a +  # a ~ + a * a