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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- Spring '11
- Recursion, Call stack, Forth, work tape, unique accepting configuration, unique starting configuration