Related papers: P vs NP Problem in the field anthropology
The relationship between the complexity classes P and NP is a question that has not yet been answered by the Theory of Computation. The existence of a language in NP, proven not to belong to P, is sufficient evidence to establish the…
In this paper we discusses the relationship between the known classes P and NP. We show that the difficulties in solving problem "P versus NP" have methodological in nature. An algorithm for solving any problem is sensitive to even small…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
NP complete problem is one of the most challenging issues. The question of whether all problems in NP are also in P is generally considered one of the most important open questions in mathematics and theoretical computer science as it has…
This paper discusses why P and NP are likely to be different. It analyses the essence of the concepts and points out that P and NP might be diverse by sheer definition. It also speculates that P and NP may be unequal due to natural laws.
We claim to resolve the P=?NP problem via a formal argument for P=NP.
Against the background of what has been termed a reproducibility crisis in science, the NLP field is becoming increasingly interested in, and conscientious about, the reproducibility of its results. The past few years have seen an…
I describe three geometric approaches to resolving variants of P v. NP, present several results that illustrate the role of group actions in complexity theory, and make a first step towards completely geometric definitions of complexity…
Complexity theory as practiced by physicists and computational complexity theory as practiced by computer scientists both characterize how difficult it is to solve complex problems. Here it is shown that the parameters of a specific model…
We study the P versus NP problem through properties of functions and monoids, continuing the work of [3]. Here we consider inverse monoids whose properties and relationships determine whether P is different from NP, or whether injective…
A novel approach to complex problems has been previously applied to graph classification and the graph equivalence problem. Here we consider its applications to a wide set of NP complete problems, namely, those of finding a subgraph g…
We survey a collective achievement of a group of researchers: the PCP Theorems. They give new definitions of the class \np, and imply that computing approximate solutions to many \np-hard problems is itself \np-hard. Techniques developed to…
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…
In this article, we discuss the question of whether P equals NP, we do not follow the line of research of many researchers, which is to try to find such a problem Q, and the problem Q belongs to the class of NP-complete, if the problem Q is…
We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The…
Physicists study a wide variety of phenomena creating new interdisciplinary research fields by applying theories and methods originally developed in physics in order to solve problems in economics, social science, biology, medicine,…
The resolution of the P vs. NP problem, a cornerstone in computational theory, remains elusive despite extensive exploration through mathematical logic and algorithmic theory. This paper takes a novel approach by integrating information…
In this article, I focus on the resiliency of the P=?NP problem. The main point to deal with is the change of the underlying logic from first to second-order logic. In this manner, after developing the initial steps of this change, I can…
Can the computational complexity theory of computer science and mathematics say something new about unresolved problems in quantum physics? Particularly, can the P versus NP question in the computational complexity theory be a factor in the…
Ambiguity is an critical component of language that allows for more effective communication between speakers, but is often ignored in NLP. Recent work suggests that NLP systems may struggle to grasp certain elements of human language…