  The notion of nondeterminism has disappeared from the current definition of
NP, which has led to ambiguities in understanding NP, and caused fundamental
difficulties in studying the relation P versus NP. In this paper, we question
the equivalence of the two definitions of NP, the one defining NP as the class
of problems solvable by a nondeterministic Turing machine in polynomial time,
and the other defining NP as the class of problems verifiable by a
deterministic Turing machine in polynomial time, and reveal cognitive biases in
this equivalence. Inspired from a famous Chinese paradox white horse is not
horse, we further analyze these cognitive biases. The work shows that these
cognitive biases arise from the confusion between different levels of
nondeterminism and determinism, due to the lack of understanding about the
essence of nondeterminism. Therefore, we argue that fundamental difficulties in
understanding P versus NP lie firstly at cognition level, then logic level.

Computational Complexity