# Understanding of SPACE in non deterministic Turing Machines

Let's consider the following situation. We have a finitie alphabet $A$. Let $A = \{a_1, .., a_k\}$ We consider words over $A$ of length exactly $n$. I am trying to solve some problem and I am going to:

Generate every word using non-deterministic Turing Machine. And, for every generated word make a computation $C$. that uses only constant space and linear time. So, it seems that we have to remember (for a moment) generated word. I mean the situation that we have to generate word $w$ and then make a computation $C$ on $w$.

The scheme of Turing machine looks like: The question is: Is my Turing machine NPSPACE? I have a problem with thinking about space complexity when it comes to nondterministic TM.

• The time complexity on inputs of size $n$ is the maximum number of steps that the machine executes before halting over all inputs of size $n$ and all guesses.
• The space complexity on inputs of size $n$ is the maximum number of tape cells that the machine uses over all inputs of size $n$ and all guesses.