## The ultimate non-deterministic Turing machine

How Turing machines work?
Given an input (w), a Turing machine is in its initial state (q0), this being its first configuration (C0=q0w) through the computation. Then, it’s going through the unique sequence C0, C1, … Ci, Ci+1 until it reaches its last configuration, that being the one with q∈{qaccept,qreject}.

Now, the computation it’s said that it’s based on an algorithm (it’s having rules). Then again, it’s said that a NTM “may have a set of rules that prescribes more than one action for a given situation” and it’s choosing the right one every time. How it’s doing that it’s not important.

But, what if the algorithm is “write the answer”? Just like that! We assume that the algorithm for a NTM is similar to the algorithms for a DTM… but, having this possibility of choosing the right next state and symbol to write, why not a straight way (the straightest way) for finding the answer?

From this point of view, the number of steps (time) a NTM runs is the length of the answer.