What is NP? - Interpretation of a Chinese paradox "white horse is not horse"

Abstract

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.