Related papers: Testing idealness in the filter oracle model

We consider filtering for a continuous-time, or asynchronous, stochastic system where the full distribution over states is too large to be stored or calculated. We assume that the rate matrix of the system can be compactly represented and…

There are numbers k and s and a URM program A(n,m) satisfying the following conditions. 1. If A(n,m) halts, then Cn(m) diverges. 2. For all n, C_k(n) = A(n,n) and C_s(n) = C_k(s). 3. A(k,s) halts and for all n, A(s,n) diverges. Here C_n(_)…

We study the problem of determining exactly the number of defective items in an adaptive Group testing by using a minimum number of tests. We improve the existing algorithm and prove a lower bound that shows that the number of tests in our…

Codd's rule of entity integrity stipulates that every table has a primary key. Hence, the attributes of the primary key carry unique and complete value combinations. In practice, data cannot always meet such requirements. Previous work…

When are two algorithms the same? How can we be sure a recently proposed algorithm is novel, and not a minor variation on an existing method? In this paper, we present a framework for reasoning about equivalence between a broad class of…

We use Rokhlin's Theorem on the uniqueness of canonical systems to find a new way to establish connections between Function Theory in the unit disk and rank one perturbations of self-adjoint or unitary operators. In the n-dimensional case,…

Craig interpolation is a fundamental property of classical and non-classic logics with a plethora of applications from philosophical logic to computer-aided verification. The question of which interpolants can be obtained from an…

Connectivity is a fundamental structural property of matroids, and has been studied algorithmically over 50 years. In 1974, Cunningham proposed a deterministic algorithm consuming $O(n^{2})$ queries to the independence oracle to determine…

An archetypal problem discussed in computer science is the problem of searching for a given number in a given set of numbers. Other than sequential search, the classic solution is to sort the list of numbers and then apply binary search.…

Clustering is an unsupervised technique of Data Mining. It means grouping similar objects together and separating the dissimilar ones. Each object in the data set is assigned a class label in the clustering process using a distance measure.…

Since the groundbreaking work of the Kalman filter in the 1960s, considerable effort has been devoted to various discrete time filters for dynamic state estimation, especially including dozens of different types of suboptimal…

We consider offsets of a union of convex objects. We aim for a filtration, a sequence of nested cell complexes, that captures the topological evolution of the offsets for increasing radii. We describe methods to compute a filtration based…

Reliable tracking algorithms are essential for automated driving. However, the existing consistency measures are not sufficient to meet the increasing safety demands in the automotive sector. Therefore, this work presents a novel method for…

We prove the consistency of a singular cardinal $\lambda$ with small value of the ultrafilter number $u_\lambda$, and arbitrarily large value of $2^\lambda$.

Many cluster similarity indices are used to evaluate clustering algorithms, and choosing the best one for a particular task remains an open problem. We demonstrate that this problem is crucial: there are many disagreements among the…

We introduce axiomatically the ring $\bf{Z}_\kappa$ of the Euclidean integers, that can be viewed as the ``integral part" of the field $\mathbb{E}$ of Euclidean numbers of [4], where the transfinite sum of ordinal indexed $\kappa$-sequences…

We consider the following scheduling problem. A system is composed of $n$ processors drawn from a pool of $N$. The processors can become faulty while in operation and faulty processors never recover. A report is issued whenever a fault…

Let f:A-->B be a covering map. We say A has e filtered ends with respect to f (or B) if for some filtration {K_n} of B by compact subsets, A - f^{-1}(K_n) "eventually" has e components. The main theorem states that if Y is a (suitable) free…

Let $A$, $B$, and $C$ be three $n\times n$ matrices. We investigate the problem of verifying whether $AB=C$ over the ring of integers and finding the correct product $AB$. Given that $C$ is different from $AB$ by at most $k$ entries, we…

We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this framework…