CSCI 8610	     Topics in Theoretical Computer Science       Fall 2006

		       	        Homework set #3

		     Due by 5:00 PM on Thursday, October 5

These problems are from Chapter 5 of the notes by Shallit except for the 
last one, on removing left-recursion.

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Exc. numbers 4, 5, 6, and 10 (20 points each)

Left-recursion (20 points):  show how to modify the method given on page 125 of
  the notes to remove immediate left-recursion so that it works correctly when
  E --> epsilon is one of the E-rules.  You may assume that there is no other
  left-recursion involving E.  The goal then is to modify the E-rules so as to
  give an equivalent CFG having no left-recursion (immediate or not) involving
  E.  A secondary goal is to avoid an exponential increase in the size of the 
  set of E-rules, as can happen when a wholesale removal of epsilon rules is
  carried out.  The size of a rule with body w is 1+|w|, and these are added
  up over all E-rules and all X-rules for any new X added in order to remove 
  left-recursion among the E-rules.