Related papers: An Improved Physical ZKP for Nonogram and Nonogram…
A $d$-defective $k$-painting game on a graph $G$ is played by two players: Lister and Painter. Initially, each vertex is uncolored and has $k$ tokens. In each round, Lister marks a chosen set $M$ of uncolored vertices and removes one token…
Let $G$ be a graph without 4-cycles and 5-cycles. We show that the problem to determine whether $G$ is $(0,k)$-colorable is NP-complete for each positive integer $k.$ Moreover, we construct non-$(1,k)$-colorable planar graphs without…
In this paper we have proposed a new test for pixel randomness using non-parametric method in statistics. In order to validate this new non-parametric test we have designed an encryption scheme based on 2D cellular automata. The strength of…
We propose an algorithm for determining the zeros of the electric conductivity in large molecular nanonstructures such as graphene sheets. To this end, we employ the inverse graph method, whereby non-zeros of the Green's functions are…
A zk-SNARK is a protocol that lets one party, the prover, prove to another party, the verifier, that a statement about some privately-held information is true without revealing the information itself. This paper describes technical…
In an undirected graph, a proper (k,i)-coloring is an assignment of a set of k colors to each vertex such that any two adjacent vertices have at most i common colors. The (k,i)-coloring problem is to compute the minimum number of colors…
We present a protocol that transforms any quantum multi-prover interactive proof into a nonlocal game in which questions consist of logarithmic number of bits and answers of constant number of bits. As a corollary, this proves that the…
A homomorphism from a graph $X$ to a graph $Y$ is an adjacency preserving mapping $f:V(X) \rightarrow V(Y)$. We consider a nonlocal game in which Alice and Bob are trying to convince a verifier with certainty that a graph $X$ admits a…
Elliptic Curve Cryptography (ECC) is an attractive alternative to conventional public key cryptography, such as RSA. ECC is an ideal candidate for implementation on constrained devices where the major computational resources i.e. speed,…
Wiesner's unforgeable quantum money scheme is widely celebrated as the first quantum information application. Based on the no-cloning property of quantum mechanics, this scheme allows for the creation of credit cards used in authenticated…
This paper presents a short and simple proof of the Four-Color Theorem that can be utterly checkable by human mathematicians, without computer assistance. The new key idea that has allowed it and the global structure of the proof are…
We introduce an uncertainty-aware graph representation framework for learning to guide planning in Partially Observable Markov Decision Processes (POMDPs). Unlike existing approaches that require domain or problem size specific neural…
By testing the classical correlation violation between two systems, the random number can be expanded and certified without applying classical statistical method. In this work, we propose a new random number expansion protocol without…
This paper investigates an extremely classic NP-complete problem: How to determine if a graph G, where each vertex has a degree of at most 4, can be 3-colorable(The research in this paper focuses on graphs G that satisfy the condition where…
Zero forcing is a combinatorial game played on a graph with a goal of turning all of the vertices of the graph black while having to use as few "unforced" moves as possible. This leads to a parameter known as the zero forcing number which…
A graph is unichord free if it does not contain a cycle with exactly one chord as its subgraph. In [3], it is shown that a graph is unichord free if and only if every minimal vertex separator is a stable set. In this paper, we first show…
A hole is a chordless cycle with at least four vertices. A pan is a graph which consists of a hole and a single vertex with precisely one neighbor on the hole. An even hole is a hole with an even number of vertices. We prove that a (pan,…
Shape correspondence is a fundamental problem in computer graphics and vision, with applications in various problems including animation, texture mapping, robotic vision, medical imaging, archaeology and many more. In settings where the…
A theoretical framework of quantum no-key (QNK) protocol has been presented. As its applications, we develop three kinds of QNK protocols: the practical QNK protocols, the QNK protocol based on quantum perfect encryption, and the QNK…
A hole in a graph G is an induced cycle of length at least four; an antihole is a hole in the complement of G. In 2005, Chudnovsky, Cornuejols, Liu, Seymour and Vuskovic showed that it is possible to test in polynomial time whether a graph…