  In this paper, we interpret NDTM (NonDeterministic Turing Machine) used to
define NP by tracing to the source of NP. Originally NP was defined as the
class of problems solvable in polynomial time by a NDTM in the theorem of Cook,
where the NDTM was represented as Query Machine of essence Oracle. Later a
model consisting of a guessing module and a checking module was proposed to
replace the NDTM. This model of essence TM has a fundamental difference from
the NDTM of essence Oracle, but people still use the term NDTM to designate
this model, which leads to the disguised displacement of NDTM and produces out
the verifier-based definition of NP as the class of problems verifiable in
polynomial time by a TM (Turing Machine). This verifier-based one has been then
accepted as the standard definition of NP where comes from the famous
equivalence of the two definitions of NP. Since then the notion of
nondeterminism is lost from NP, which causes ambiguities in understanding NP
and then great difficulties in solving the P versus NP problem. Since NP is
originally related with Oracle that comes from the work of Turing work about
Computability, it seems quite necessary to trace back to the work of Turing and
clarify further the issue about NP.
