NP is not AL and P is not NC is not NL is not L

1. Overview This paper talk about that NP is not AL and P, P is not NC, NC is not NL, and NL is not L. The point about this paper is the depend relation of the problem that need other problem's result to compute it. I show the structure of depend relation that could divide each complexity classes. 2. The condition to emulate the TM by using UTM We will begin by considering the important nature of Turing Machine (TM) in this paper. Definition 1. I will use the term " Action Configuration " to the part of the computation configuration that decide next transition. Action configuration include the information of state, transition function, position (head), and read memory (tape alphabet at head). I will use the term " Action configuration have all information to yield the next configuration, therefore we can make the universal turing machine (UTM) that emulate TM by using the information include the action configuration. Definition 2. I will use the term " VTM " as " Virtual Turing Machine " to the TM that UTM emulate. Theorem 3. Log space is necessary and sufficient to record action configuration. Proof. The memory space that is required with the action configuration would be as follows: state and transition function is determined for each TM, and TM can record in the constant space. And position can record with log space. And read memory can record with constant space. Therefore, UTM can record TM's action configuration into log space. Next, I talk about the sharing of the information of VTM. Theorem 4. In NTM, VTM that execute nondeterministic branches does not share information and result each other. If VTM share the information and result, VTM must be executed in same branch. Proof. VTM that execute non deterministic branches converges to single VTM. The VTM is one of these branches. Another branches do not exist, and these VTM can not affects the single VTM. Therefore, VTM that execute non deterministic branches does not share information and result each other.