A General NP Completeness Theorem
نویسنده
چکیده
A detailed model of a random access computation over an ab stract domain is presented and the existence of an NP complete problem is proven under broad conditions which unify Cook s theorem and recent results in the real number model by Blum Shub and Smale
منابع مشابه
P != NP Proof
This paper demonstrates that P ≠ NP. The way was to generalize the traditional definitions of the classes P and NP, to construct an artificial problem (a generalization to SAT: The XG-SAT, much more difficult than the former) and then to demonstrate that it is in NP but not in P (where the classes P and NP are generalized and called too simply P and NP in this paper, and then it is explained wh...
متن کاملAn integer programming proof of Cook’s theorem of NP-completeness
The theory of NP-completeness has its roots in a foundational result by Cook, who showed that Boolean satisfiability (SAT) is NP-complete and thus unlikely to admit an efficient solution. We prove an analogous result using binary integer programming in the place of SAT. The proof gives deeper insight into the theory of NP-completeness to operations researchers for whom the language of integer p...
متن کاملLecture 1 : Course Overview and Turing machine complexity
1. Basic properties of Turing Machines (TMs), Circuits & Complexity 2. P, NP, NP-completeness, Cook-Levin Theorem. 3. Hierarchy theorems, Circuit lower bounds. 4. Space complexity: PSPACE, PSPACE-completeness, L, NL, Closure properties 5. Polynomial-time hierarchy 6. #P and counting problems 7. Randomized complexity 8. Circuit lower bounds 9. Interactive proofs & PCP Theorem Hardness of approxi...
متن کاملNear NP-Completeness for Detecting p-adic Rational Roots in One Variable
We show that deciding whether a sparse univariate polynomial has a p-adic rational root can be done in NP for most inputs. We also prove a polynomial-time upper bound for trinomials with suitably generic p-adic Newton polygon. We thus improve the best previous complexity upper bound of EXPTIME. We also prove an unconditional complexity lower bound of NP-hardness with respect to randomized reduc...
متن کاملThe Kleene-Rosser Paradox, The Liar's Paradox&A Fuzzy Logic Programming Paradox Imply SAT is (NOT) NP-complete
After examining the P versus NP problem against the Kleene-Rosser paradox of the λ-calculus [94], it was found that it represents a counterexample to NP-completeness. We prove that it contradicts the proof of Cook's theorem. A logical formalization of the liar's paradox leads to the same result. This formalization of the liar's paradox into a computable form is a 2-valued instance of a fuzzy lo...
متن کامل