CSCI 6610		  Automata and Formal Languages		     Spring 2004

			        Homework set #2

		       Due by 2:30 PM on Friday, February 6  

            These exercises/problems are all from the text by Sipser.

NOTES: "Show" always means PROVE in the exercise/problem descriptions.
       Be sure to consult the note below for any problem followed by a * in the 
       listing, as this indicates a hint and/or directions.  Hints are optional,
       but all other directions such as "modify", "let", "do",... are mandatory.
--------------------------------------------------------------------------------

	4.17  (15 pts.)
	5.9   (10 pts.)
	5.10  (15 pts.)
	5.11* (10 pts.)
	5.14* (15 pts.)
	5.15  (15 pts.)
	6.7*  (20 pts.)

* Hint for 5.11:  You can use J from 5.10 for your example B.

* Hint for 5.14:  You can reduce A_TM to LEFT_TM, the latter being the language 
	you are to define and show is not recursive.  Try a mapping 
	<M,w> |---> <M',#w> where # is a new symbol not in the tape alphabet 
	of M.  The # symbol at the start of the tape will make it easy for M' 
	to simulate M without accidently attempting to move off the left end of 
	the tape.  Of course if M does accept w then the simulation can turn
	control over to a state which will eventually try to move the head off 
	the left end of the tape.
	
* For 6.7: Also prove that if A and B are both Turing reducible to some set C
	then your set J is also Turing reducible to C.
	Hint: you can use the idea in Sipser's problem 5.10, where A_TM and its
	complement are coded into a set J.