Due: Thursday, October 20 by 11 pm. Please use the dropbox linked from the CSE401 homework web page to submit your homework online. Any common format like pdf or doc/docx is fine, or you can submit a scanned copy of your work as long as it is legible. 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. Give an unambiguous grammar for each of the following languages. (Hint: One way of verifying that a grammar is unambiguous is to run it through a LALR parser generator like Yacc, Bison, or CUP and get no conflicts. You are not required to do this, however.)
   
   
   1. Statement blocks in Pascal or ML where the semicolons separate the statements:
      { statement ; { statement ; statement } ; statement }
   2. Statement blocks in C or Java where the semicolons terminate the statements:
      { expression ; { expression ; expression ; } expression ; }
   3. Balanced parentheses and square brackets. Example:
      ([[](()[()][])])[]
   
   
2. Given the following grammar:
   
   S ::= ( L ) | x
   L ::= L , S | S
   
   
   1. Give a left-most derivation of (x, (x, x)) .
   2. Give a right-most derivation of (x, (x, x)) .
   3. Show the steps that a shift-reduce parser goes through when it parses (x, x, x). That is, show the contents of the stack and remaining input at each step.
   4. Suppose we replace the left-recursive production L::=L,S with a right-recursive one L::=S,L. What general effect does this have on the depth of the stack during a shift-reduce parse? (You might work through the parse of (x, x, x) again to see what changes.)
      
      
3. 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?
   
   
4. (Appel) Write a grammar for English sentences using the words
   

   time  arrow  banana  flies  like  a  an  the  fruit

   and the semicolon. Be sure to include all the senses (noun, verb, etc.) of each word. Then show that this grammar is ambiguous by exhibiting more than one parse tree for the sentence "time flies like an arrow; fruit flies like a banana".)