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What is Cook's theorem?
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