CSE 401/M501 24au (Mini-)Homework 3 - LL Grammars

Due: Monday, October 28 by 11:59 pm. At most one late day allowed so we can make solutions available in time to study for the midterm exam. Please use Gradescope (gradescope.com, also linked from the CSE 401/M501 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.

• Unreadable solutions cannot be graded--no blurry photos, poor contrast, or illegible handwriting, please.
• Type-written solutions are encouraged but not required.
• If possible, don't split the solution to a problem across a page break.

We suggest you show your work to help us award partial credit if appropriate, and for TA sanity. You should do this assignment individually.

1. 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.
   
   
2. 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