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EECS 395-23 - Assignment 2 1. Let L be a language accepted by a deterministic RAM machine in time t(n). Show there is a k such that L is accepted by...

I need only third exercise from attached.
EECS 395-23 – Assignment 2 1. Let L be a language accepted by a deterministic RAM machine in time t ( n ). Show there is a k such that L is accepted by a multi-tape Turing machine in time t k ( n ). 2. Show that for any space-constructible s 1 ( n ) and s 2 ( n ) such that s 1 ( n ) = o ( s 2 ( n )), NSPACE( s 1 ( n )) ( NSPACE( s 2 ( n )). Hint: Use the fact that nondeterministic space is closed under complement. 3. Let NTISP( t ( n ) ,s ( n )) be the set of problems solvable by a nonde- terministic Turing machine using t ( n ) time and s ( n ) space. Show NTISP( t ( n ) ,s ( n )) DSPACE( s ( n ) log t ( n )). 4. Show that for some real a > 1, the function s ( n ) = n a is not space- constructible. 5. Show that for all reals a and b with 1 a < b , DSPACE( n a ) ( DSPACE( n b ).
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This question was asked on Mar 19, 2010.

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