Honors Theory of Computation, Spring'00.

HOMEWORK 2:

Out: Jan 31
Due: Feb 7

	==================================================	
	IMPORTANT:  you MUST answer each question 
	within the page limitation specified 
	(with reasonable size handwriting).  
	When necessary, summarize the method or arguments.

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	YOU MUST CHOOSE TO HAND IN SOLUTIONS FOR
		EITHER	QUESTIONS (1) and (2)
	OR	QUESTION (3). 
	HOWEVER, I STRONGLY ENCOURAGE YOU TO SOLVE
	TO YOUR OWN SATISFACTION THE OTHER
	QUESTION(S) THAT YOU DO NOT HAND IN.
	==================================================	


(1) Solve Problem 2.8.7 (Chapter 2, page 53 of Text)
	
	One page limit.
	This concerns a 2-dimensional TM.

(2) Recall the corollary to Theorem 2.6 (page 47) that
	if we can decide a language L in nondeterministic
	time f then we can decide L in deterministic
	time df for some d > 1
	Prove the same result, except that we replace the
	word ``decide'' by ``accept''.
	NOTE: This is illustrates the remark that that ``acceptance
	complexity'' and ``decision complexity'' usually have
	equivalent theorems. 
	
	Half page limit.

(3) Solve Problem 2.8.11 (Chapter 2, page 54)

	Two pages limit.
	Do only parts (a) to (d).

	This concerns Regular Languages, which I assume
	you have seen in some previous course (any
	undergraduate theory course will have this material).
	This is a good chance to review regular languages
	(these are favorite topics in exam questions).