On Sipser page 279:(adsbygoogle = window.adsbygoogle || []).push({}); If a branch of an NTM uses f(n) space, we know that f(n) is the maximum number of (input) tape cells that it scans on any branch of its computation for an input of length n. But we don't know how many times it runs back and forth over those cells before the computation branch finishes. So how does he determine that such a branch may run for [itex]2^{O(f(n))}[/itex] stepsSavitch's theorem

For any function [tex]\begin{equation*}\begin{split}f: N \longrightarrow N, \;\text{where}\;f(n) \geq n,\\

\text{NSPACE}(f(n)) \subseteq \text{SPACE}f^2(n)).\end{split}\end{equation}[/tex]

Proof idea: We need to simulate an f(n) space NTM deterministically. A naive approach is to proceed by trying all the branches of the NTM's computation, one by one. The simulation needs to keep track of which branch it is currently trying so that it is able to go on to the next one. But a branch that uses f(n) space may run for [itex]2^{O(f(n))}[/itex] steps, and each step may be a nondeterministic choice...only? Why not, for example, [itex]2^{O(f(n^2))}[/itex]? Or maybe some much lower limit? I don't know. Any ideas where this [itex]2^{O(f(n))}[/itex] comes from?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# More space complexity: Savitch's Theorem

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads for More space complexity | Date |
---|---|

I Need to know the Topology on the Space of all Theories? | Oct 10, 2017 |

A Nonlinear regression in two or more independent variables | Jul 6, 2017 |

A Advanced Data Fitting - More than Simple Regressions | Jun 22, 2017 |

I What is more probable? | Nov 13, 2016 |

I Probability of getting 3 heads or more in 20 coin flips | Jun 19, 2016 |

**Physics Forums - The Fusion of Science and Community**