Related papers: A Brief Note on a Recent Claim About NP-Hard Probl…
The notion of nondeterminism has disappeared from the current definition of NP, which has led to ambiguities in understanding NP, and caused fundamental difficulties in studying the relation P versus NP. In this paper, we question the…
We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and…
A discursive, non-technical, analysis is made of some of the basic issues that arise in almost any approach to quantum gravity, and of how these issues stand in relation to recent developments in the field. Specific topics include the…
In this paper, we consider a fractional p-Laplacian system of equations in the entire space RN with doubly critical singular nonlinearities involving a local critical Sobolev term together with a nonlocal Choquard critical term; the problem…
We survey results on the formalization and independence of mathematical statements related to major open problems in computational complexity theory. Our primary focus is on recent findings concerning the (un)provability of complexity…
In this paper we prove that the \textsc{Min-Bisection} problem is NP-hard on \emph{unit disk graphs}, thus solving a longstanding open question.
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…
This paper initially aimed at proposing a proof that quasi-dense logics have f.m.p, but it contains a major flaw, unfixable.
In a brief note posted recently, the authors of arXiv:1503.07813 raised some concerns on our arxiv:1502.03821, recently published in Nature Physics. We thank them for the interest in our work and respond here to their criticisms.
It is commonplace, in the literature, to find that the Bekenstein-Hawking entropy has been endowed with having an explicit statistical interpretation. In the following essay, we discuss why such a viewpoint warrants a certain degree of…
We close three open problems in the separation complexity of valid inequalities for the knapsack polytope. Specifically, we establish that the separation problems for extended cover inequalities, (1,k)-configuration inequalities, and weight…
When it comes to NP, its natural definition, its wide applicability across scientific disciplines, and its timeless relevance, the writing is on the wall: There can be only one. Quantum NP, on the other hand, is clearly the apple that fell…
Very brief summary of the most recent developments in an area of QED corrections to the parity nonconservation in atoms is presented. Main conclusion - experimental results of Wood et al do not contradict the standard model
We examine a proof by Craig Alan Feinstein that P is not equal to NP. We present counterexamples to claims made in his paper and expose a flaw in the methodology he uses to make his assertions. The fault in his argument is the incorrect use…
In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.
Reducing the NP-problems to the convex/linear analysis on the Birkhoff polytope.
We present an approximation notion for NP-hard optimization problems represented by binary functions. We prove that (assuming P != NP) the new notion is strictly stronger than FPTAS, but strictly weaker than having a polynomial-time…
We consider $p$-weak differentiable structures that were recently introduced by the first and last named authors, and prove that the product of $p$-weak charts is a $p$-weak chart. This implies that the product of two spaces with a $p$-weak…
The aim of this short note is to clarify some of the claims made in the comparison made in [S. Lloyd, On the uncomputability of the spectral gap, arXiv:1602.05924] between our recent result [T.S. Cubitt, D. Perez-Garcia, M.M. Wolf,…
In my ("not a summary") talk at the Hard Probes 2006 conference, I gave "a personal and surely biased view on only a few of the many open questions on quarkonium and electromagnetic probes". Some of the points reported in that talk are…