Search results for "computational complexity."
showing 10 items of 245 documents
Proving The Power Of Postselection
2011
It is a widely believed, though unproven, conjecture that the capability of postselection increases the language recognition power of both probabilistic and quantum polynomial-time computers. It is also unknown whether polynomial-time quantum machines with postselection are more powerful than their probabilistic counterparts with the same resource restrictions. We approach these problems by imposing additional constraints on the resources to be used by the computer, and are able to prove for the first time that postselection does augment the computational power of both classical and quantum computers, and that quantum does outperform probabilistic in this context, under simultaneous time an…
Forrelation
2014
We achieve essentially the largest possible separation between quantum and classical query complexities. We do so using a property-testing problem called Forrelation, where one needs to decide whether one Boolean function is highly correlated with the Fourier transform of a second function. This problem can be solved using 1 quantum query, yet we show that any randomized algorithm needs Ω(√(N)log(N)) queries (improving an Ω(N[superscript 1/4]) lower bound of Aaronson). Conversely, we show that this 1 versus Ω(√(N)) separation is optimal: indeed, any t-query quantum algorithm whatsoever can be simulated by an O(N[superscript 1-1/2t])-query randomized algorithm. Thus, resolving an open questi…
Exact affine counter automata
2017
We introduce an affine generalization of counter automata, and analyze their ability as well as affine finite automata. Our contributions are as follows. We show that there is a language that can be recognized by exact realtime affine counter automata but by neither 1-way deterministic pushdown automata nor realtime deterministic k-counter automata. We also show that a certain promise problem, which is conjectured not to be solved by two-way quantum finite automata in polynomial time, can be solved by Las Vegas affine finite automata. Lastly, we show that how a counter helps for affine finite automata by showing that the language MANYTWINS, which is conjectured not to be recognized by affin…
Almost disjoint spanning trees: relaxing the conditions for completely independent spanning trees
2017
International audience; The search of spanning trees with interesting disjunction properties has led to the introduction of edge-disjoint spanning trees, independent spanning trees and more recently completely independent spanning trees. We group together these notions by dening (i, j)-disjoint spanning trees, where i (j, respectively) is the number of vertices (edges, respectively) that are shared by more than one tree. We illustrate how (i, j)-disjoint spanning trees provide some nuances between the existence of disjoint connected dominating sets and completely independent spanning trees. We prove that determining if there exist two (i, j)-disjoint spanning trees in a graph G is NP-comple…
A two-armed bandit collective for hierarchical examplar based mining of frequent itemsets with applications to intrusion detection
2014
Published version of a chapter in the book: Transactions on Computational Collective Intelligence XIV. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-662-44509-9_1 In this paper we address the above problem by posing frequent item-set mining as a collection of interrelated two-armed bandit problems. We seek to find itemsets that frequently appear as subsets in a stream of itemsets, with the frequency being constrained to support granularity requirements. Starting from a randomly or manually selected examplar itemset, a collective of Tsetlin automata based two-armed bandit players - one automaton for each item in the examplar - learns which items should be included in …
Route to chaos in the weakly stratified Kolmogorov flow
2019
We consider a two-dimensional fluid exposed to Kolmogorov’s forcing cos(ny) and heated from above. The stabilizing effects of temperature are taken into account using the Boussinesq approximation. The fluid with no temperature stratification has been widely studied and, although relying on strong simplifications, it is considered an important tool for the theoretical and experimental study of transition to turbulence. In this paper, we are interested in the set of transitions leading the temperature stratified fluid from the laminar solution [U∝cos(ny),0, T ∝ y] to more complex states until the onset of chaotic states. We will consider Reynolds numbers 0 < Re ≤ 30, while the Richardson numb…
"Table 2" of "Study of Dimuon Production in Photon-Photon Collisions and Measurement of QED Photon Structure Functions at LEP"
2001
The measured QED photon structure function at Q**2 = 120 GeV for the combine SAT and STIC data.
Exact results for accepting probabilities of quantum automata
2001
One of the properties of Kondacs-Watrous model of quantum finite automata (QFA) is that the probability of the correct answer for a QFA cannot be amplified arbitrarily. In this paper, we determine the maximum probabilities achieved by QFAs for several languages. In particular, we show that any language that is not recognized by an RFA (reversible finite automaton) can be recognized by a QFA with probability at most 0.7726...
Quantum search of spatial regions
2003
Can Grover's algorithm speed up search of a physical region - for example a 2-D grid of size sqrt(n) by sqrt(n)? The problem is that sqrt(n) time seems to be needed for each query, just to move amplitude across the grid. Here we show that this problem can be surmounted, refuting a claim to the contrary by Benioff. In particular, we show how to search a d-dimensional hypercube in time O(sqrt n) for d at least 3, or O((sqrt n)(log n)^(3/2)) for d=2. More generally, we introduce a model of quantum query complexity on graphs, motivated by fundamental physical limits on information storage, particularly the holographic principle from black hole thermodynamics. Our results in this model include a…
Interactions of pharmaceutical companies with world countries, cancers and rare diseases from Wikipedia network analysis
2019
AbstractUsing the English Wikipedia network of more than 5 million articles we analyze interactions and interlinks between the 34 largest pharmaceutical companies, 195 world countries, 47 rare renal diseases and 37 types of cancer. The recently developed algorithm using a reduced Google matrix (REGOMAX) allows us to take account both of direct Markov transitions between these articles and also of indirect transitions generated by the pathways between them via the global Wikipedia network. This approach therefore provides a compact description of interactions between these articles that allows us to determine the friendship networks between them, as well as the PageRank sensitivity of countr…