CSE P 501 23au Homework 3 - LR and LL Grammars & Parsing

Due: Monday, October 23 by 11 pm. Please use Gradescope (gradescope.com, also linked from the CSE P 501 resources web page) to submit your homework online. Gradescope's web site has several instructional videos and help pages to outline the process, and this guide has specific information about scanning and uploading pdf files containing assignments.

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1. The following is a grammar that generates epithets (E). An epithet is a description (D). A description can be either a trait (T) or a simile (S). Similies are of the form "trait like animal" (A).
   
   E ::= D
   D ::= T | S
   S ::= T like A
   T ::= quick | strong
   A ::= bunny | ox
   
   
   1. Construct the LR(0) state diagram and parse table for this grammar.
   2. Calculate FIRST, FOLLOW, and nullable for each non-terminal.
   3. Construct the SLR parse table.
   4. Is this grammar LR(0)? SLR?
   
   
2. Consider the following grammar:
   
   A ::= s C n g | ε
   B ::= C r | t
   C ::= B i | t
   
   Does this grammar satisfy the LL(1) condition? Justify your answer. If it does not, change the grammar to make it LL(1) without changing the language that it generates.
   
   
3. Write a grammar that generates the straight-line code language given below, but that is suitable for LL(1) parsing. That is, eliminate the ambiguity, eliminate the left recursion, and (if necessary) left-factor.
   
   S ::= S ; S
   S ::= id := E
   S ::= print( L )
   E ::= id
   E ::= num
   E ::= E + E
   E ::= ( S , E )
   L ::= E
   L ::= L , E