CSAT is not in P

11/02/2021

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by   Fabio Romano, et al.

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In this paper we have to demonstrate that if we claim to have an algorithm that solves CSAT in polynomial time with a DTM (Deterministic Turing Machine), then we have to admit that: there is a counterexample that invalidates the correctness of the algorithm. This is because if we suppose that it can prove that an elenkhos formula (a formula that lists the negated codes of all models) is a contradiction, and if we change exactly a specific boolean variable of that formula, then we have proven that: in this case the algorithm will always fail.