Related papers: A Brief Note on a Recent Claim About NP-Hard Probl…
I review some of the main results on hard diffraction, in their relation to QCD, and indicate some of the strengths and weaknesses of the arguments. I also make some suggestions for future work.
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…
This is a short note to answer Brukner's objection [see arXiv:2107.03513] to Rovelli's theory and concerning the preferred basis problem.
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
Recently I posted a paper entitled "External observer reflections on QBism". As any external observable, I was not able to reflect some features of QBism properly. Therefore comments which I received from one of its creators, C. Fuchs, are…
We give some reductions among problems in (nonnegative) weighted #CSP which restrict the class of functions that needs to be considered in computational complexity studies. Our reductions can be applied to both exact and approximate…
We survey the average-case complexity of problems in NP. We discuss various notions of good-on-average algorithms, and present completeness results due to Impagliazzo and Levin. Such completeness results establish the fact that if a certain…
In this paper, we provide a sharp remainder term for the general weighted discrete $p$-Hardy inequality. By simply choosing weights and specifying $1<p<\infty$, we are able to recover the identity by Krej{\v{c}}i{\v{r}}{\'\i}k-\v{S}tampach…
Recent results in the field of Heavy Quarkonia are reviewed, with results either providing new precision measurements or addressing key unanswered questions.
The following problem is NP-hard: given a regular expression $E$, decide if $E^*$ is not co-finite.
How hard is it to invert NP-problems? We show that all superlinearly certified inverses of NP problems are coNP-hard. To do so, we develop a novel proof technique that builds diagonalizations against certificates directly into a circuit.
We indicate that an argument of da Costa and Doria in fact proves P=NP. This observation makes their argument appear dubious. We isolate a weak version of one of their lemmas which would already prove P=NP. We point out that even this weak…
Some q-analysis variants of Hardy type inequalities of the form \int_0^b (x^{\alpha-1} \int_0^x t^{-\alpha} f(t) d_qt)^p d_qx \leq C \int_0^b f^p(t) d_qt with sharp constant C are proved and discussed. A similar result with the…
In this note we comment on remarks about our recent effort to understand the specificities of the Boltzmann equation in the context of the alternative theories of gravity with non-minimal coupling between curvature and matter.
In a recent paper, Banuls and Bernabeu have claimed the existence of a new form of indirect CP violation which would have its most prominent manifestation in the $B_d$-$\bar B_d$ system. I analyse this claim in detail. I emphasize the fact…
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.…
Some recent developments in the heavy quark theory are briefly reviewed. The main emphasis is put on interrelation between HQET and OPE. The notion of duality and deviations from duality are discussed in detail.
The classical PCP theorem is arguably the most important achievement of classical complexity theory in the past quarter century. In recent years, researchers in quantum computational complexity have tried to identify approaches and develop…
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…
I review some of the salient issues connected to CP-violation and weak decays. In particular, I focus on recent and forthcoming tests of the CKM model and discuss the accuracy one can expect to achieve in B-decays for the parameters of this…