TL;DR
This paper claims to prove that P is not equal to NP by showing SAT cannot be in P within a specific formal logical framework, establishing the separation as true and provable.
Contribution
It introduces a formal logical proof within a first-order theory framework that SAT is not in P, implying P ≠ NP.
Findings
SAT is not in P, as proven in a formal logical system
P ≠ NP is true and provable within the proposed framework
The proof relies on a specific extension of a first-order theory of computing
Abstract
SAT is not in P, is true and provable in a simply consistent extension B' of a first order theory B of computing, with a single finite axiom characterizing a universal Turing machine. Therefore, P is not equal to NP, is true and provable in a simply consistent extension B" of B.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · semigroups and automata theory · Logic, programming, and type systems