Search results for " Complexity theory"
showing 10 items of 131 documents
Non-intersecting Complexity
2006
A new complexity measure for Boolean functions is introduced in this article. It has a link to the query algorithms: it stands between both polynomial degree and non-deterministic complexity on one hand and still is a lower bound for deterministic complexity. Some inequalities and counterexamples are presented and usage in symmetrisation polynomials is considered.
Quantum Computing: A Way to Break Complexity?
2003
The perception of time is given by the happening of some events that determines a variation in the state of the observed system. In this sense a computation, i.e. a set of well defined transformations that, starting from an initial state (the input) brings to a final state (the output), can be considered a time generator. Each ticking of the clock corresponds to the computer changes of its states. The speed of computation leads to a different perception of time as well as traveling by airplanes changed the perception of spatial distances.
Fluted Logic with Counting
2021
The fluted fragment is a fragment of first-order logic in which the order of quantification of variables coincides with the order in which those variables appear as arguments of predicates. It is known that the fluted fragment possesses the finite model property. In this paper, we extend the fluted fragment by the addition of counting quantifiers. We show that the resulting logic retains the finite model property, and that the satisfiability problem for its (m+1)-variable sub-fragment is in m-NExpTime for all positive m. We also consider the satisfiability and finite satisfiability problems for the extension of any of these fragments in which the fluting requirement applies only to sub-form…
Superresolved imaging of remote moving targets.
2006
We present a superresolving approach that allows one to exceed the diffraction limit and recover highly resolved contours of moving targets from a sequence of low-resolution images. The presented approach is suitable for remote sensing applications. The resolution decoding algorithm that is used to recover the high-resolution features of the target can be run partially via optical means and that way can be used to reduce the required computational complexity.
Optimal Impulse Control Problems and Linear Programming
2009
Optimal impulse control problems are, in general, difficult to solve. A current research goal is to isolate those problems that lead to tractable solutions. In this paper, we identify a special class of optimal impulse control problems which are easy to solve. Easy to solve means that solution algorithms are polynomial in time and therefore suitable to the on-line implementation in real-time problems. We do this by using a paradigm borrowed from the Operations Research field. As main result, we present a solution algorithm that converges to the exact solution in polynomial time. Our approach consists in approximating the optimal impulse control problem via a binary linear programming proble…
The Crane Beach Conjecture
2002
A language L over an alphabet A is said to have a neutral letter if there is a letter e/spl isin/A such that inserting or deleting e's from any word in A* does not change its membership (or non-membership) in L. The presence of a neutral letter affects the definability of a language in first-order logic. It was conjectured that it renders all numerical predicates apart from the order predicate useless, i.e., that if a language L with a neutral letter is not definable in first-order logic with linear order then it is not definable in first-order. Logic with any set /spl Nscr/ of numerical predicates. We investigate this conjecture in detail, showing that it fails already for /spl Nscr/={+, *…
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 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.
Rotation-Invariant Texture Retrieval via Signature Alignment Based on Steerable Sub-Gaussian Modeling
2008
This paper addresses the construction of a novel efficient rotation-invariant texture retrieval method that is based on the alignment in angle of signatures obtained via a steerable sub-Gaussian model. In our proposed scheme, we first construct a steerable multivariate sub-Gaussian model, where the fractional lower-order moments of a given image are associated with those of its rotated versions. The feature extraction step consists of estimating the so-called covariations between the orientation subbands of the corresponding steerable pyramid at the same or at adjacent decomposition levels and building an appropriate signature that can be rotated directly without the need of rotating the im…
A Learning Automata Based Solution to Service Selection in Stochastic Environments
2010
Published version of a paper published in the book: Trends in Applied Intelligent Systems. Also available on SpringerLink: http://dx.doi.org/10.1007/978-3-642-13033-5_22 With the abundance of services available in today’s world, identifying those of high quality is becoming increasingly difficult. Reputation systems can offer generic recommendations by aggregating user provided opinions about service quality, however, are prone to ballot stuffing and badmouthing . In general, unfair ratings may degrade the trustworthiness of reputation systems, and changes in service quality over time render previous ratings unreliable. In this paper, we provide a novel solution to the above problems based …