Search results for " complexity."
showing 10 items of 603 documents
A Dynamic Distributed Algorithm for Multicast Path Setup
2005
In the past few years, there has been a considerable work on multicast route selection techniques, with the aim to design scalable protocols which can guarantee an efficient use of network resources. Steiner tree-based multicast algorithms produce optimal trees, but they are prohibitively expensive. For this reason, heuristic methods are generally employed. Conventional centralized Steiner heuristics provide effective solutions, but they are unpractical for large networks, since they require a complete knowledge of the network topology. In this paper, we propose a new distributed approach that is efficient and suitable for real network adoption. Performance evaluation indicates that it outp…
Occupational cognitive complexity and episodic memory in old age
2021
The aim of this study was to investigate occupational cognitive complexity of main lifetime occupation in relation to level and 15-year change in episodic memory recall in a sample of older adults (≥ 65 years, n = 780). We used latent growth curve modelling with occupational cognitive complexity (O*NET indicators) as independent variable. Subgroup analyses in a sample of middle-aged (mean: 49.9 years) men (n = 260) were additionally performed to investigate if a general cognitive ability (g) factor at age 18 was predictive of future occupational cognitive complexity and cognitive performance in midlife. For the older sample, a higher level of occupational cognitive complexity was related to…
Analyticity of a restricted formality
2020
International audience; The Kontsevich formality can be viewed as a non-linear map ℱ from the L∞ algebra of poly-vector fields on ℝd to the space of poly-differential operators. The space of the half-homogenous poly-vector fields is a sub-L∞ algebra. We prove here that the restriction of ℱto this subspace is weakly analytic.
Quadratically Tight Relations for Randomized Query Complexity
2020
In this work we investigate the problem of quadratically tightly approximating the randomized query complexity of Boolean functions R(f). The certificate complexity C(f) is such a complexity measure for the zero-error randomized query complexity R0(f): C(f) ≤R0(f) ≤C(f)2. In the first part of the paper we introduce a new complexity measure, expectational certificate complexity EC(f), which is also a quadratically tight bound on R0(f): EC(f) ≤R0(f) = O(EC(f)2). For R(f), we prove that EC2/3 ≤R(f). We then prove that EC(f) ≤C(f) ≤EC(f)2 and show that there is a quadratic separation between the two, thus EC(f) gives a tighter upper bound for R0(f). The measure is also related to the fractional…
On the class of languages recognizable by 1-way quantum finite automata
2000
It is an open problem to characterize the class of languages recognized by quantum finite automata (QFA). We examine some necessary and some sufficient conditions for a (regular) language to be recognizable by a QFA. For a subclass of regular languages we get a condition which is necessary and sufficient. Also, we prove that the class of languages recognizable by a QFA is not closed under union or any other binary Boolean operation where both arguments are significant.
Local softening of information geometric indicators of chaos in statistical modeling in the presence of quantum-like considerations
2013
In a previous paper (C. Cafaro et al., 2012), we compared an uncorrelated 3D Gaussian statistical model to an uncorrelated 2D Gaussian statistical model obtained from the former model by introducing a constraint that resembles the quantum mechanical canonical minimum uncertainty relation. Analysis was completed by way of the information geometry and the entropic dynamics of each system. This analysis revealed that the chaoticity of the 2D Gaussian statistical model, quantified by means of the Information Geometric Entropy (IGE), is softened or weakened with respect to the chaoticity of the 3D Gaussian statistical model due to the accessibility of more information. In this companion work, we…
The class of languages recognizable by 1-way quantum finite automata is not closed under union
2000
In this paper we develop little further the theory of quantum finite automata (QFA). There are already few properties of QFA known, that deterministic and probabilistic finite automata do not have e.g. they cannot recognize all regular languages. In this paper we show, that class of languages recognizable by QFA is not closed under union, even not under any Boolean operation, where both arguments are significant.
Grover’s Search with Faults on Some Marked Elements
2018
Grover’s algorithm is a quantum query algorithm solving the unstructured search problem of size [Formula: see text] using [Formula: see text] queries. It provides a significant speed-up over any classical algorithm [3]. The running time of the algorithm, however, is very sensitive to errors in queries. Multiple authors have analysed the algorithm using different models of query errors and showed the loss of quantum speed-up [2, 6]. We study the behavior of Grover’s algorithm in the model where the search space contains both faulty and non-faulty marked elements. We show that in this setting it is indeed possible to find one of marked elements in [Formula: see text] queries. We also analyze…
Quantum Lower Bound for Graph Collision Implies Lower Bound for Triangle Detection
2015
We show that an improvement to the best known quantum lower bound for GRAPH-COLLISION problem implies an improvement to the best known lower bound for TRIANGLE problem in the quantum query complexity model. In GRAPH-COLLISION we are given free access to a graph $(V,E)$ and access to a function $f:V\rightarrow \{0,1\}$ as a black box. We are asked to determine if there exist $(u,v) \in E$, such that $f(u)=f(v)=1$. In TRIANGLE we have a black box access to an adjacency matrix of a graph and we have to determine if the graph contains a triangle. For both of these problems the known lower bounds are trivial ($\Omega(\sqrt{n})$ and $\Omega(n)$, respectively) and there is no known matching upper …
Quantum versus classical query complexity of relation
2011
This paper investigates the computability of mathematical relations in a quantum query model. The important task in complexity theory is to find examples with a large gap between classical and quantum algorithm complexity of the same computational problem. We present new results in quantum query algorithm design that allow achieving a large separation between classical and quantum query complexity of a specific relation. We demonstrate an example where quantum query algorithm for a finite relation needs more than two times fewer queries than the best possible classical analogue. We also show that relation can be extended to infinite family of relations with an input of general size N.