Related papers: Some Results on the Counterfeit Coins Problem
In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.
More precise estimation of the greedy algorithm complexity for a special case of the set cover problem is given in this paper.
This is a survey of old and new problems and results in additive number theory.
This note comprises a negative resolution of the Efficient Market Hypothesis.
Pilz's conjecture states that for any finite set $A=\{a_1,a_2,\dots,a_k\}$ of positive integers and positive integer $n$ in the union of the sets $\{a_1,2a_1,\dots,na_1\},\dots, \{a_k,2a_k,\dots,na_k\}$ (considered as a multiset) at least…
In this short note we present a family of counterexamples to the King's conjecture.
A quantum money scheme enables a trusted bank to provide untrusted users with verifiable quantum banknotes that cannot be forged. In this work, we report an experimental demonstration of the preparation and verification of unforgeable…
This paper introduces the notion of multiset codes as relevant to the problem of reliable information transmission over permutation channels. The motivation for studying permutation channels comes from the effect of out of order delivery of…
The aim of this paper is to solve the "gift exchange" problem: you are one of n players, and there are n wrapped gifts on display; when your turn comes, you can either choose any of the remaining wrapped gifts, or you can "steal" a gift…
There are concerns that new approaches to the synthesis of high quality face videos may be misused to manipulate videos with malicious intent. The research community therefore developed methods for the detection of modified footage and…
Currency recognition systems often overlook usability and authenticity assessment, especially in low-resource environments where visually impaired users and offline validation are common. While existing methods focus on denomination…
Quantum protocols for coin-flipping can be composed in series in such a way that a cheating party gains no extra advantage from using entanglement between different rounds. This composition principle applies to coin-flipping protocols with…
Digital currencies primarily operate online, but there is growing interest in enabling offline transactions to improve digital inclusion. Existing offline methods struggle with double-spending risks, often limiting transaction amounts. In…
In this paper, we are concerned with the sign-changing solutions of variational inequality problems. In order to give the existence results of the sign-changing solutions for variational inequality problems, we first construct a suitable…
We devised a protocol that allows two parties, who may malfunction or intentionally convey incorrect information in communication through a quantum channel, to verify each other's measurements and agree on each other's results. This has…
The multivariate time series generated from merchant transaction history can provide critical insights for payment processing companies. The capability of predicting merchants' future is crucial for fraud detection and recommendation…
Motivated by the importance of floating-point computations, we study the problem of securely and accurately summing many floating-point numbers. Prior work has focused on security absent accuracy or accuracy absent security, whereas our…
Let k_1,...,k_d be positive integers, and D be a subset of [k_1]x...x[k_d], whose complement can be decomposed into disjoint sets of the form {x_1}x...x{x_{s-1}}x[k_s]x{x_{s+1}}x...x{x_d}. We conjecture that the number of elements of D can…
We survey the state of the union-closed sets conjecture.
Certain new inequalities for the sums of factorials are presented.