Proper complexity function: Difference between revisions
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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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Similar notions include honest function, [[space-constructible function]], and [[time-constructible function]]. |
Similar notions include honest function, [[space-constructible function]], and [[time-constructible function]]. |
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{{DEFAULTSORT:Proper Complexity Function}} |
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[[Category:Computational complexity theory]] |
[[Category:Computational complexity theory]] |
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[[Category:Articles lacking sources (Erik9bot)]] |
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Revision as of 13:54, 17 December 2009
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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.