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Title:
A Heuristic Proof of P \neq NP
Authors: Ping Wang
Abstract:The question of whether the complexity class P equals NP is a major unsolved problem in theoretical computer science. In this paper, we introduce a new language, the Add and XNOR (the negation of exclusive or (XOR)) problem, which has the simplest structure and perfect randomness, by extending the subset sum problem. We prove that P \neq NP as it shows that an exhaustive search is necessary to solve the Add and XNOR problem. That is, problems that are verifiable in polynomial time are not necessarily solvable in polynomial time.
ePrint: https://eprint.iacr.org/2024/2035
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