相关论文: Some interesting problems

The Monty Hal problem is an attractive puzzle. It combines simple statement with answers that seem surprising to most audiences. The problem was thoroughly solved over two decades ago. Yet, more recent discussions indicate that the solution…

A complete characterization of the complexity of the reachability problem for vector addition system has been open for a long time. The problem is shown to be Tower complete.

The goal of this article is to introduce some beautiful known riddles in intuitive topology; hoping to make at least some fun for the reader.

I have been asked to discuss the status of QCD. It seems to me that there are three main points to be made about the present status of QCD: $\bullet$ QCD is right, and we can do many beautiful things with it. $\bullet$ There are several…

In this note we briefly survey and propose some open problems related to isoparametric theory.

We survey recent developments in the theory of achievement sets and present a substantial collection of open problems.

Malwares are continuously growing in sophistication and numbers. Over the last decade, remarkable progress has been achieved in anti-malware mechanisms. However, several pressing issues (e.g., unknown malware samples detection) still need…

The study consists of two parts. Objective of the first part is modern language constructions responsible for algorithmically insolvability of parallelizing problem. Second part contains several ways to modify the constructions to make the…

Dynamic complexity is concerned with updating the output of a problem when the input is slightly changed. We study the dynamic complexity of Dyck reachability problems in directed and undirected graphs, where updates may add or delete…

We address the question of whether it may be worthwhile to convert certain, now classical, NP-complete problems to one of a smaller number of kernel NP-complete problems. In particular, we show that Karp's classical set of 21 NP-complete…

An updated version of this paper is available at http://arxiv.org/abs/1505.01131

A sequence of positive integers is introduced, that is proved to simultaneously solve an infinite family of related puzzles, one of which was recently featured on the popular YouTube sudoku channel \emph{Cracking the Cryptic}.

In these notes I will briefly summarize our knowledge about the dark matter problem, and emphasize the corresponding dynamical aspects. This covers a wide area of research, so I have been selective, and have concentrated on the subject of…

New cases of the multiplicity conjecture are considered.

The evolution of the user's content still remains a problem for an accurate recommendation.This is why the current research aims to design Recommender Systems (RS) able to continually adapt information that matches the user's interests.…

The main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. These problems are of general interest for discrete mathematics including a new twig of a bough of theory of…

We discuss fun problems, vaguely related to notions and theorems of a course in differential geometry. This paper can be regarded as a weekend "treasure chest" supplementing the course weekday lecture notes. The problems and solutions are…

This document is built around a list of thirty-two problems in enumeration of matchings, the first twenty of which were presented in a lecture at MSRI in the fall of 1996. I begin with a capsule history of the topic of enumeration of…

This paper gives an overview on and summarizes existing complexity and algorithmic results of some variants of the Stable Marriage and the Stable Roommates problems. The last section defines a list of stable matching problems mentioned in…

In this small paper we bring together various open problems on geometric multidimensional continued fractions.