proper complexity function
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 functions, space-constructible functions, and time-constructible functions.
References
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{{cite book |last1=Myashnikov |first1=Alexei |last2=Shpilrain |first2=Vladimir |last3=Ushakov |first3=Vladimir |title=Group-based Cryptography |date=2008 |publisher=Birkhauser |isbn=978-3-7643-8826-3 |page=28}}
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