What is Cook's theorem?

Abstract: In this paper, we make a preliminary interpretation of Cook's theorem presented in [1]. This interpretation reveals cognitive biases in the proof of Cook's theorem that arise from the attempt of constructing a formula in CNF to represent a computation of a nondeterministic Turing machine. Such cognitive biases are due to the lack of understanding about the essence of nondeterminism, and lead to the confusion between different levels of nondeterminism and determinism, thus cause the loss of nondeterminism from the NP-completeness theory. The work shows that Cook's theorem is the origin of the loss of nondeterminism in terms of 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. Therefore, we argue that fundamental difficulties in understanding P versus NP lie firstly at cognition level, then logic level.