Honors Theory of Computation, Spring'00.

HOMEWORK 3:

Out: Feb 9
Due: Feb 16

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	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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(1)  Prove the following space hierarchy theorem:

	Suppose $f,g$ are proper functions and limit of $f(n)/g(n)$
	goes to $0$ as $n$ goes to infinity.

	Then SPACE(f) is properly contained in SPACE(g).

	LIMIT: 1 page.

	HINT: follow the outline of our lecture on time hierarchy
	theorem.  You probably need to use some form of 
	following property about
	encoding of Turing machines: for each machine M there
	are infinitely distinct representations whose only
	difference lies in the existence of totally useless transitions
	in the transition function.