Related papers: Some Results on the Counterfeit Coins Problem
The Change-Making Problem is to represent a given value with the fewest coins under a given coin system. As a variation of the knapsack problem, it is known to be NP-hard. Nevertheless, in most real money systems, the greedy algorithm…
We study the problem of multiset prediction. The goal of multiset prediction is to train a predictor that maps an input to a multiset consisting of multiple items. Unlike existing problems in supervised learning, such as classification,…
The subset sum problem over finite fields is a well-known {\bf NP}-complete problem. It arises naturally from decoding generalized Reed-Solomon codes. In this paper, we study the number of solutions of the subset sum problem from a…
By some new recursive algorithms, in this paper, we will give some improvements on Waring's problem.
This paper analyzes a necessary and sufficient condition for the change-making problem to be solvable with a greedy algorithm. The change-making problem is to minimize the number of coins used to pay a given value in a specified currency…
We investigate a result on convergence of double sequences of numbers and how it extends to measurable functions.
Counterfeit products cause severe harm to public safety and health by penetrating untrusted supply chains. Numerous anti-counterfeiting techniques have been proposed, among which the use of inherent, unclonable irregularities of paper…
In this paper, we will continue the investigation of Waring's problem, and give further improvements.
Falsification is drawing attention in quality assurance of heterogeneous systems whose complexities are beyond most verification techniques' scalability. In this paper we introduce the idea of causality aid in falsification: by providing a…
In this paper, a new upper bound for the Multiple Knapsack Problem (MKP) is proposed, based on the idea of relaxing MKP to a {\em Bounded Sequential Multiple Knapsack Problem}, i.e., a multiple knapsack problem in which item sizes are…
We discuss counterintuitive aspects of probabilities for systems of identical particles obeying quantum statistics. Quantum coins and children (two level systems) and quantum dice (many level systems) are used as examples. It is emphasized…
In this note we evaluate the expectation and variance of the waiting time to complete $m$ parallel collections of coupons, in the case of coupons which arrives independently, one by one and with equal probabilities.
A major drawback in deploying central bank digital currencies (CDBC) is the offline puzzle, which requires that a CBDC must keep the provision given by cash, and, simultaneously, avoid double-spending, counterfeiting, and other issues. The…
We study a labeled variant of the classical Coupon Collector Problem (CCP), recently introduced by Tan et al., where coupons arrive in groups and only the set of labels is revealed. The goal is to determine the expected number of group…
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
We generalize the problem of coin flipping to more than two outcomes and parties. We term this problem dice rolling, and study both its weak and strong variants. We prove by construction that in quantum settings (i) weak N-sided dice…
As in many coin puzzles, we have several identical-looking coins, with one of them fake and the rest real. The real coins weigh the same. Our fake coin is special in that it can change its weight. The coin can pretend to be a real coin, a…
A quantitative check of weak efficiency in US dollar/German mark exchange rates is developed using high frequency data. We show the existence of long term return anomalies. We introduce a technique to measure the available information and…
We give some results and conjectures about recurrence relations for certain sequences of binomial sums.
We present new counterexamples, which provide stronger limitations to sums-differences statements than were previously known. The main idea is to consider non-uniform probability measures.