Proper complexity function
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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.
- Alexei Myasnikov, Vladimir Shpilrain, Alexander Ushakov. Group-based Cryptography. Birkhäuser Verlag, 2008, p.28