Related papers: Solution to the Counterfeit Coin Problem and its G…
We investigate a coin-weighing puzzle that appeared in the all-Russian math Olympiad in 2000. We liked the puzzle because the methods of analysis differ from classical coin-weighing puzzles. We generalize the puzzle by varying the number of…
A simple computer-based algorithm has been developed to identify pre-modern coins minted from the same dies, intending mainly coins minted by hand-made dies designed to be applicable to images taken from auction websites or catalogs. Though…
In this note, we introduce a distributed twist on the classic coupon collector problem: a set of $m$ collectors wish to each obtain a set of $n$ coupons; for this, they can each sample coupons uniformly at random, but can also meet in…
We consider the problem of revealing a small hidden lattice from the knowledge of a low-rank sublattice modulo a given sufficiently large integer -- the {\em Hidden Lattice Problem}. A central motivation of study for this problem is the…
Verifying equivalence between two quantum circuits is a hard problem, that is nonetheless crucial in compiling and optimizing quantum algorithms for real-world devices. This paper gives a Turing reduction of the (universal) quantum circuits…
Weighted counting problems are a natural generalization of counting problems where a weight is associated with every computational path of polynomial-time non-deterministic Turing machines and the goal is to compute the sum of the weights…
In this paper, we revisit the much studied problem of Pattern Matching with Swaps (Swap Matching problem, for short). We first present a graph-theoretic model, which opens a new and so far unexplored avenue to solve the problem. Then, using…
While canonical quantization solves many problems there are some problems where it fails. A close examination of the classical/quantum connection leads to a new connection that permits quantum and classical realms to coexist, as is the case…
In mutation testing the question whether a mutant is equivalent to its program is important in order to compute the correct mutation score. Unfortunately, answering this question is not always possible and can hardly be obtained just by…
The classic Coupon-Collector Problem (CCP) is generalized to the extent that each coupons serves certain "purposes". Only basic probability theory is used. Centerpiece rather is an algorithm that efficiently counts all $k$-element…
We present an analysis of Wiesner's quantum money scheme, as well as some natural generalizations of it, based on semidefinite programming. For Wiesner's original scheme, it is determined that the optimal probability for a counterfeiter to…
We study the Min-Weighted Sum Bin Packing problem, a variant of the classical Bin Packing problem in which items have a weight, and each item induces a cost equal to its weight multiplied by the index of the bin in which it is packed. This…
Automatic authentication of paper money has been targeted. Indian bank notes are taken as reference to show how a system can be developed for discriminating fake notes from genuine ones. Image processing and pattern recognition techniques…
We study the problem of universal quantum cloning -- taking several identical copies of a pure but unknown quantum state and producing further copies. While it is well known that it is impossible to perfectly reproduce the state, how well…
Publicly verifiable quantum money is a protocol for the preparation of quantum states that can be efficiently verified by any party for authenticity but is computationally infeasible to counterfeit. We develop a cryptographic scheme for…
We discuss the possibility of creating money that is physically impossible to counterfeit. Of course, "physically impossible" is dependent on the theory that is a faithful description of nature. Currently there are several proposals for…
There are many papers written on the Two Envelopes Problem that usually study some of its variations. In this paper we will study and compare the most significant variations of the problem. We will see the correct decisions for each player…
Protocols for tossing a common coin play a key role in the vast majority of implementations of consensus. Even though the common coins in the literature are usually \emph{fair} (they have equal chance of landing heads or tails), we focus on…
Expanding on recent results of another an algorithm is presented that provides solution to the Frobenius Coin Problem in worst case O(n^2) in the magnitude of the largest denomination.
We propose a solution to the quantum measurement paradox by first identifying its classical counterpart.