Dave Hanold
CS 536
Lecture Notes -- 02/22/99
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** Read Chapter 4
** Parser project to be handed out on Wednesday

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* How do scanner generators operate?

  1.  Translate regular expression to NFA 
  2.  Convert the NFA to a DFA (construct set of states)
  3.  Optimize DFA (reduce states)

  example: (aa|aaaaa)+
  --  subdivide into sets of 2 and 5
  --  any even # (or odd # greater than 5) will work


  --  FA: (()) means a final state
        
       a     a       a     a       a       a       a       a       a
-->(1)-->(2)-->((3))-->(4)-->((5))-->((6))-->((7))-->((8))-->((9))-->((10))
								      ^ |
								      | |a
                                                                       -

* When are 2 states in a DFA equivalent?
  -- Criteria for Merging States: ONLY IF THEY HAVE IDENTICAL FUTURE
                                  BEHAVIOR
			
* GREEDY ALGORITHM (to merge states of a DFA):
  
  1.  Merge together all final states into a group G1; merge together all
      nonfinal states into a group G2

  2.  REPEAT:
        Let G = any state set = {S1, S2, ..., Sn}
	Let C = any character               c        c
	Let G' = {t1, t2, ..., tn} where S1-->t1, S2-->t2     

 	if G' is not entirely contained in some existing group,
	  then split G' into new groups such that Si and Sj remain
	  together iff ti and tj are in the same group

      --example:

       a     b
-->(1)-->(2)-->((3)) 
      |
      |c     d     b
      -->(4)-->(5)-->((6))

	G1 = [3, 6]
        G2 = [1, 2, 4, 5]

	--We can pull out the states numbered 1 and 4 since their outcomes
	  are unique.
        --The algorithm gives the maximum reduction of states:
 		 a       b
          -->(1)-->(2,5)-->((3,6))
	      |      ^
             c|      |d
               ->(4)-

      --example (aa|aaaaa)+ yields:

       a     a       a     a 
-->(1)-->(2)-->((3))-->(4)-->((5-10))
			       |  ^
 			      a|  |
                                --
      
  3.  Generate scanner code in executable form
      --Regular expression rules followed by appropriate code


* CREATE TRANSITION TABLE FOR OPTIMIZED DATA

  (aa|aaaaa)+ example:

        Char 'a'
State 1     2
      2     3	
      3     4
      4     5 
      5     5

  is implemented as a switch statement:
	case 1: {Java Code A}
		break;
	case 2: {Java Code B}
		break;

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