Related papers: The P versus NP Problem
This paper has been withdrawn by the authors, because it has been made obsolete by the detailed expositions in our papers in arXiv:0812.4885 (the mathematics part) and arXiv:0812.4737 (the economics part).
The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…
$P \overset{\text{?}}{=} NP$ or $P\ vs\ NP$ is the core problem in computational complexity theory. In this paper, we proposed a definition of linear correlation of derived matrix and system, and discussed the linear correlation of $P$ and…
The computational complexity of the "cluster minimization problem" is revisited [L. T. Wille and J. Vennik, J. Phys. A 18, L419 (1985)]. It is argued that the original NP-hardness proof does not apply to pairwise potentials of physical…
This paper talk about that NP is not AL and P, P is not NC, NC is not NL, and NL is not L. The point about this paper is the depend relation of the problem that need other problem's result to compute it. I show the structure of depend…
This paper has been withdrawn by the author, due to possible counter-examples.
This paper considers the question of P = NP in context of the polynomial time SAT algorithm. It posits proposition dependent on existence of conjectured problem that even where the algorithm is shown to solve SAT in polynomial time it…
The subject logic in computer science should entail proof theoretic applications. So the question arises whether open problems in computational complexity can be solved by advanced proof theoretic techniques. In particular, consider the…
This article has been removed by arXiv administrators due to falsified authorship.
This paper was withdrawn by arXiv admin because it plagiarizes "Chen, Wen Gu(PRC-BIAP); Lu, Shan Zhen(PRC-BJN) The commutators of fractional integrals on Besov spaces. Acta Math. Sin. (Engl. Ser.) 20 (2004), no. 3, 405--414."
This chapter delves into the realm of computational complexity, exploring the world of challenging combinatorial problems and their ties with statistical physics. Our exploration starts by delving deep into the foundations of combinatorial…
This short note present a "proof" of $P\neq NP$. The "proof" with double quotation marks is to indicate that we do not know whether the proof is correct or not (We're confused because we do know in which we make the mistakes).
The P versus NP problem is addressed in a context of provability and limitations on the possibility of finding sound axioms for formal theories. It is shown that if the term "constructible theory" is defined in a way which satisfies certain…
In this paper, we inquire the key concept P-reduction in Cook's theorem and reveal that there exists the fallacy of definition in P-reduction caused by the disguised displacement of NDTM from Oracle machine to Turing machine. The definition…
This article is a survey of recent developments in, and a tutorial on, the approach to P v. NP and related questions called Geometric Complexity Theory (GCT). It is written to be accessible to graduate students. Numerous open questions in…
We address two sets of long-standing open questions in probability theory, from a computational complexity perspective: divisibility of stochastic maps, and divisibility and decomposability of probability distributions. We prove that finite…
Are P and NP provably inseparable ? Take a look at some unorthodox, guilty mentioned folklore and related unpublished results.
The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase…
This paper has been removed by arXiv administrators because it plagiarizes hep-th/0311050, gr-qc/0306101, gr-qc/9601044, gr-qc/0511106, gr-qc/0303034, and gr-qc/0212018.
Geometric complexity theory (GCT) is an approach to the $P$ vs. $NP$ and related problems. A high level overview of this research plan and the results obtained so far was presented in a series of three lectures in the Institute of Advanced…