# A uniform computability model to define time and space complexity (even in the sublinear case) [closed]

To define time complexity the Turing machine model with only one tape (for input, work and output) is used. This TMM is also used to define the $s(n)$-space complexity for $s(n) \ge n$.

But if $s(n)$ is sublinear e.g. $s(n)=\log(n)$ this TMM does not work. So usually a new TMM is used: the Turing machine get a new tape, the input tape where only reading is allowed (nor deleting or writing).

1. Is there a computation model which is suitable to define time complexity and space complexity (even if the space function is sublinear)?
2. Is it possible to find a "global" $s(n)$-space complexity definition for the "classical" Turing machines with only one tape?

## closed as off-topic by Emil Jeřábek, Jan Johannsen, Damiano Mazza, Kaveh, Mohammad Al-TurkistanyJul 25 '17 at 13:58

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