Related papers: The P versus NP Problem

This paper describes several new problems and ideas concerning algebraic geometry and complexity theory. It first uses the idea of coloring graphs with elements of finite fields. This procedure then shows that graph coloring problems can be…

This paper presents the following results on sets that are complete for NP. 1. If there is a problem in NP that requires exponential time at almost all lengths, then every many-one NP-complete set is complete under length-increasing…

In this paper, we prove that the MaxCut problem is NP-complete on permutation graphs, settling a long-standing open problem that appeared in the 1985 column of the "Ongoing Guide to NP-completeness" by David S. Johnson.

Withdrawn by arXiv administration because authors have forged affiliations and acknowledgements, and have not adequately responded to charges [hep-th/9912039] of unattributed use of verbatim material.

We propose a new approach to solve an NP complete problem by means of stochastic limit.

A polynomial algorithm is obtained for the NP-complete linear ordering problem.

This is the old version of this project. Please find the new version at 1906.12233.

This paper has been withdrawn by the author(s), due to double submission. You can find it under: physics/0208019

P vs NP problem is the most important unresolved problem in the field of computational complexity. Its impact has penetrated into all aspects of algorithm design, especially in the field of cryptography. The security of cryptographic…

We study statistical properties of an NP-complete problem, the subset sum, using the methods and concepts of statistical mechanics. The problem is a generalization of the number partitioning problem, which is also an NP-complete problem and…

We show that the problem of determining the feasibility of quadratic systems over $\mathbb{C}$, $\mathbb{R}$, and $\mathbb{Z}$ requires exponential time. This separates P and NP over these fields/rings in the BCSS model of computation.

Withdrawn by arXiv administration because authors have forged affiliations and acknowledgements, and have not adequately responded to charges [hep-th/9912039] of unattributed use of verbatim material.

This paper calls attention to the current state of the probability (P) domain which presents weak points at the mathematical level and more significant flaws at the application level. Popper notices how fundamental issues raised in quantum…

This paper has been removed by arXiv administrators because of overlap with gr-qc/0303034 and others. This paper also has excessive overlap with the following papers also written by the authors or their collaborators: gr-qc/0509047,…

We show that some mathematical results and their negations are both deducible. The derived contradictions indicate the inconsistency of current mathematics. This paper is an updated version of arXiv:math/0606635v3 with additional results…

This paper has been removed by arXiv administrators because it plagiarizes gr-qc/0303034 and gr-qc/0212018.

The K-way vertex cut problem} consists in, given a graph G, finding a subset of vertices of a given size, whose removal partitions G into the maximum number of connected components. This problem has many applications in several areas. It…

I survey methods from differential geometry, algebraic geometry and representation theory relevant for the permanent v. determinant problem from computer science, an algebraic analog of the P v. NP problem.

Over the course of the last 50 years, many questions in the field of computability were left surprisingly unanswered. One example is the question of $P$ vs $NP\cap co-NP$. It could be phrased in loose terms as "If a person has the ability…

Withdrawn; replaced by longer, more detailed paper quant-ph/0010065.