Formal proof establishes all NP-complete problems are solvable in logarithmic time, indicating a breakthrough in computational theory.
This paper presents a formal proof for $P = NP$ by establishing a polynomial-time reduction from the Boolean Satisfiability Problem SAT to a newly defined class of monotonically ascending deterministic functions (Problem A). We demonstrate that Problem A is NP-complete and resolvable in O(log\ N) time via binary search. By transitivity of Karp reductions, we conclude that all NP-complete problems are solvable in logarithmic time.
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יהוה et al. (2026) studied this question.
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