Related papers: On Searching for Small Kochen-Specker Vector Syste…
Similarity measures based purely on word embeddings are comfortably competing with much more sophisticated deep learning and expert-engineered systems on unsupervised semantic textual similarity (STS) tasks. In contrast to commonly used…
The $k$-Even Set problem is a parameterized variant of the Minimum Distance Problem of linear codes over $\mathbb F_2$, which can be stated as follows: given a generator matrix $\mathbf A$ and an integer $k$, determine whether the code…
A new theory-independent noncontextuality inequality is presented [Phys. Rev. Lett. 115, 110403 (2015)] based on Kochen-Specker (KS) set without imposing the assumption of determinism. By proposing novel noncontextuality inequalities, we…
Given a graph $G=(V, E)$ and a positive integer $k$, in Maximum $k$-Order Bounded Component Set (Max-$k$-OBCS), it is required to find a vertex set $S \subseteq V$ of maximum size such that each component in the induced graph $G[S]$ has at…
We give a method for exhaustive generation of a huge number of Kochen-Specker contextual sets, based on the 600-cell, for possible experiments and quantum gates. The method is complementary to our previous parity proof generation of these…
We investigate small geometric configurations that furnish observable-based proofs of the Kochen-Specker theorem. Assuming that each context consists of the same number of observables and each observable is shared by two contexts, it is…
In this paper we study two directions of extending the classical Erd\H os-Ko-Rado theorem which states that any family of $k$-element subsets of the set $[n] = \{1,\ldots,n\}$ in which any two sets intersect, has cardinality at most…
The Kochen-Specker theorem is one of the fundamental no-go theorems in quantum theory. It has far-reaching consequences for all attempts trying to give an interpretation of the quantum formalism. In this work, we examine the hypotheses…
We propose a kind of reverse Kochen-Specker theorem that amounts to generating orthomodular lattices (OMLs) with exactly one state that do not admit properties of the Hilbert space. We apply MMP algorithms to obtain smallest OMLs with 35…
In this paper, we consider the problem of finding weak independent sets in a distributed network represented by a hypergraph. In this setting, each edge contains a set of r vertices rather than simply a pair, as in a standard graph. A…
In the Feedback Vertex Set problem, one is given an undirected graph $G$ and an integer $k$, and one needs to determine whether there exists a set of $k$ vertices that intersects all cycles of $G$ (a so-called feedback vertex set). Feedback…
We address the following problem: Given a complete $k$-partite geometric graph $K$ whose vertex set is a set of $n$ points in $\mathbb{R}^d$, compute a spanner of $K$ that has a ``small'' stretch factor and ``few'' edges. We present two…
Semi-device-independent (SDI) randomness generation protocols based on Kochen-Specker contextuality offer the attractive features of compact devices, high rates, and ease of experimental implementation over fully device-independent (DI)…
A proof of the generalized Kochen-Specker theorem in two dimensions due to Cabello and Nakamura is extended to all higher dimensions. A set of 18 states in four dimensions is used to give closely related proofs of the generalized…
In the Orthogonal Vectors problem (OV), we are given two families $A, B$ of subsets of $\{1,\ldots,d\}$, each of size $n$, and the task is to decide whether there exists a pair $a \in A$ and $b \in B$ such that $a \cap b = \emptyset$.…
We discuss the topological properties of the independence complex of Kneser graphs, Ind(KG$(n, k))$, with $n\geq 3$ and $k\geq 1$. By identifying one kind of maximal simplices through projective planes, we obtain homology generators for the…
For a digraph $G$, a set $F\subseteq V(G)$ is said to be a feedback vertex set (FVS) if $G-F$ is acyclic. The problem of finding a smallest FVS is NP-hard. We present a matrix scaling technique for finding feedback vertex sets in…
Only finite precision measurements are experimentally reasonable, and they cannot distinguish a dense subset from its closure. We show that the rational vectors, which are dense in S^2, can be colored so that the contradiction with hidden…
Quantum contextuality supports quantum computation and communication. One of its main vehicles is hypergraphs. The most elaborated are the Kochen-Specker ones, but there is also another class of contextual sets that are not of this kind.…
For a field $\mathbb{F}$ and integers $d$ and $k$, a set ${\cal A} \subseteq \mathbb{F}^d$ is called $k$-nearly orthogonal if its members are non-self-orthogonal and every $k+1$ vectors of ${\cal A}$ include an orthogonal pair. We prove…