Related papers: Physical Zero-Knowledge Proof for Ripple Effect
Understanding and reasoning about physics is an important ability of intelligent agents. We develop the PHYRE benchmark for physical reasoning that contains a set of simple classical mechanics puzzles in a 2D physical environment. The…
A fast Non-linear and non-iterative learning and classification algorithm is synthesized and validated. This algorithm named the "Reverse Ripple Effect(R.R.E)", achieves 100% learning accuracy but is computationally expensive upon…
A famous result in game theory known as Zermelo's theorem says that "in chess either White can force a win, or Black can force a win, or both sides can force at least a draw". The present paper extends this result to the class of all…
A random jigsaw puzzle is constructed by arranging $n^2$ square pieces into an $n \times n$ grid and assigning to each edge of a piece one of $q$ available colours uniformly at random, with the restriction that touching edges receive the…
Spin Hall Effect is relativistic quantum mechanical effect which enables non-magnetic materials show magnetic phenomena without the application of a magnetic field. With spin Hall Effect, one can realize spintronics devices operating purely…
We study a well-known technique of using absoluteness for giving choice-free proofs to some statements which are known to be provable with the axiom of choice. The idea is to reduce the problem to an inner model where the axiom of choice…
We analyze the computational complexity of the many types of pencil-and-paper-style puzzles featured in the 2016 puzzle video game The Witness. In all puzzles, the goal is to draw a simple path in a rectangular grid graph from a start…
This paper investigates mixed strategies in dynamic games with perfect information. We present an example to show that a player may obtain higher payoff by playing mixed strategy. By contrast, the main result of the paper shows that every…
We consider a problem, which we call secure grouping, of dividing a number of parties into some subsets (groups) in the following manner: Each party has to know the other members of his/her group, while he/she may not know anything about…
Inspired by a common technique for shuffling a deck of cards on a table without riffling, we formalize the pile shuffle and investigate its capabilities as a sorting device. Our study is novel in that we consider pile shuffle in three…
Duplicate detection is the problem of identifying whether a given item has previously appeared in a (possibly infinite) stream of data, when only a limited amount of memory is available. Unfortunately the infinite stream setting is…
This paper studies how spatial thinking interacts with simplicity in [informal] proof, by analysing a set of example proofs mainly concerned with Ferrers diagrams (visual representations of partitions of integers, and comparing them to…
Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of $n$ objects scales factorially in $n$. One recent way that has been used to reduce storage complexity has been to exploit…
The positive zero forcing number of a graph is a graph parameter that arises from a non-traditional type of graph colouring, and is related to a more conventional version of zero forcing. We establish a relation between the zero forcing and…
In this paper, we prove that if a finite number of rectangles, every of which has at least one integer side, perfectly tile a big rectangle then there exists a strategy which reduces the number of these tiles (rectangles) without violating…
We consider the following game that has been used as a way of testing claims of extrasensory perception (ESP). One is given a deck of $mn$ cards comprised of $n$ distinct types each of which appears exactly $m$ times: this deck is shuffled…
In each step of the overlapping cycles shuffle on $n$ cards, a fair coin is flipped which determines whether the $m$th card or the $n$th card is moved to the top of the deck. Angel, Peres, and Wilson showed the following interesting fact:…
It is shown that the toy Turing Tumble, suitably extended with an infinitely long game board and unlimited supply of pieces, is Turing-Complete. This is achieved via direct simulation of a Turing machine. Unlike previously informally…
We study a popular puzzle game known variously as Clickomania and Same Game. Basically, a rectangular grid of blocks is initially colored with some number of colors, and the player repeatedly removes a chosen connected monochromatic group…
Several differential equations usually appearing in mathematical physics are solved through a power series expansion, which reduces in solving difference equations. In this paper a probability problem is presented whose solution follows a…