Proper complexity function: Difference between revisions
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{{Unreferenced|date=December 2009}} |
{{Unreferenced|date=December 2009}} |
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A '''proper complexity function''' is a function ''f'' mapping a [[natural number]] to a natural number such that: |
A '''proper complexity function''' is a function ''f'' mapping a [[natural number]] to a natural number such that: |
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* ''f'' is nondecreasing; |
* ''f'' is nondecreasing; |
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[[Category:Computational complexity theory]] |
[[Category:Computational complexity theory]] |
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<ref>Alexei Myasnikov, Vladimir Shpilrain, Alexander Ushakov. Group-based Cryptography. Birkhäuser Verlag, 2008, p.28 </ref> |
<ref>Alexei Myasnikov, Vladimir Shpilrain, Alexander Ushakov. Group-based Cryptography. Birkhäuser Verlag, 2008, p.28 </ref> |
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Revision as of 13:54, 6 May 2014
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A proper complexity function is a function f mapping a natural number to a natural number such that:
- f is nondecreasing;
- there exists a k-string Turing machine M such that on any input of length n, M halts after O(n + f(n)) steps, uses O(f(n)) space, and outputs f(n) consecutive blanks.
If f and g are two proper complexity functions, then f + g, fg, and 2f, are also proper complexity functions.
Similar notions include honest function, space-constructible function, and time-constructible function. [1]
References
- ^ Alexei Myasnikov, Vladimir Shpilrain, Alexander Ushakov. Group-based Cryptography. Birkhäuser Verlag, 2008, p.28