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savitch

savitch - this function can be computed recursivelv as...

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Let M be a nondeterministic machine that always halts and runs in space ,S(n). Then, M runs in at most T : qngs(n) steps for q states and g svmbols in the tape alphabet. Now, if necessary, reprogram M to erase the work tape and end in a particular state when it accepts. As before, a configuration records the contents of the work tape, the state of the machine, and the position of the head on the input tape. To simplify things we pad each configuration to have length,S(n). So, there is a unique starting configuration C" for a given input and a unique accepting configuration C". The question is: Is there a legal sequence of moves from C" to Co? Define the boolean function / that takes as arguments two configura- tions Cr andC2 and an integer i such that f (C1,C2,i,) is TRUE if M cart
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Unformatted text preview: this function can be computed recursivelv as follows: The boolean function onestep determines whether configuration c1 follows from configuration Cz according to the rules of M. So, we build a deterministic machine and ask it for the answer to f (C",Co,?). How much storage does this use? The recursive program can use a stack for storage, pushing a "snapshot" of the subroutine's variables each time it calls itself again. Each configuration and hence each snapshot uses O(^9(n)) space. The maximum number of snapshots on the stack at any one time is log ?: at each stage of the recursion, the integer is halved so that the recursion goes down only log 7 levels. Because log Z is O(S(n)). it follows that the total space needed is O((S(n)),) cells. The statement of the theorem now follows....
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