Search results for "Complex."
showing 10 items of 5824 documents
The monadic quantifier alternation hierarchy over grids and pictures
1998
The subject of this paper is the expressive power of monadic second-order logic over two-dimensional grids. We give a new, self-contained game-theoretical proof of the nonexpressibility results of Matz and Thomas. As we show, this implies the strictness of the monadic second-order quantifier alternation hierarchy over grids.
Orlicz–Sobolev extensions and measure density condition
2010
Abstract We study the extension properties of Orlicz–Sobolev functions both in Euclidean spaces and in metric measure spaces equipped with a doubling measure. We show that a set E ⊂ R satisfying a measure density condition admits a bounded linear extension operator from the trace space W 1 , Ψ ( R n ) | E to W 1 , Ψ ( R n ) . Then we show that a domain, in which the Sobolev embedding theorem or a Poincare-type inequality holds, satisfies the measure density condition. It follows that the existence of a bounded, possibly non-linear extension operator or even the surjectivity of the trace operator implies the measure density condition and hence the existence of a bounded linear extension oper…
The Descriptive Complexity Approach to LOGCFL
1999
Building upon the known generalized-quantifier-based firstorder characterization of LOGCFL, we lay the groundwork for a deeper investigation. Specifically, we examine subclasses of LOGCFL arising from varying the arity and nesting of groupoidal quantifiers. Our work extends the elaborate theory relating monoidal quantifiers to NC1 and its subclasses. In the absence of the BIT predicate, we resolve the main issues: we show in particular that no single outermost unary groupoidal quantifier with FO can capture all the context-free languages, and we obtain the surprising result that a variant of Greibach's "hardest contextfree language" is LOGCFL-complete under quantifier-free BIT-free interpre…
Uncountable classical and quantum complexity classes
2018
It is known that poly-time constant-space quantum Turing machines (QTMs) and logarithmic-space probabilistic Turing machines (PTMs) recognize uncountably many languages with bounded error (A.C. Cem Say and A. Yakaryılmaz, Magic coins are useful for small-space quantum machines. Quant. Inf. Comput. 17 (2017) 1027–1043). In this paper, we investigate more restricted cases for both models to recognize uncountably many languages with bounded error. We show that double logarithmic space is enough for PTMs on unary languages in sweeping reading mode or logarithmic space for one-way head. On unary languages, for quantum models, we obtain middle logarithmic space for counter machines. For binary la…
Online Scheduling of Task Graphs on Heterogeneous Platforms
2020
Modern computing platforms commonly include accelerators. We target the problem of scheduling applications modeled as task graphs on hybrid platforms made of two types of resources, such as CPUs and GPUs. We consider that task graphs are uncovered dynamically, and that the scheduler has information only on the available tasks, i.e., tasks whose predecessors have all been completed. Each task can be processed by either a CPU or a GPU, and the corresponding processing times are known. Our study extends a previous $4\sqrt{m/k}$ 4 m / k -competitive online algorithm by Amaris et al. [1] , where $m$ m is the number of CPUs and $k$ k the number of GPUs ( $m\geq k$ m ≥ k ). We prove that no online…
New Encodings of Pseudo-Boolean Constraints into CNF
2009
International audience; This paper answers affirmatively the open question of the existence of a polynomial size CNF encoding of pseudo-Boolean (PB) constraints such that generalized arc consistency (GAC) is maintained through unit propagation (UP). All previous encodings of PB constraints either did not allow UP to maintain GAC, or were of exponential size in the worst case. This paper presents an encoding that realizes both of the desired properties. From a theoretical point of view, this narrows the gap between the expressive power of clauses and the one of pseudo-Boolean constraints.
Timed Sets, Functional Complexity, and Computability
2012
AbstractThe construction of various categories of “timed sets” is described in which the timing of maps is considered modulo a “complexity order”. The properties of these categories are developed: under appropriate conditions they form discrete, distributive restriction categories with an iteration. They provide a categorical basis for modeling functional complexity classes and allow the development of computability within these settings. Indeed, by considering “program objects” and the functions they compute, one can obtain models of computability – i.e. Turing categories – in which the total maps belong to specific complexity classes. Two examples of this are introduced in some detail whi…
Some Common Coupled Fixed Point Results for Generalized Contraction in Complex-Valued Metric Spaces
2013
We introduce and study the notion of common coupled fixed points for a pair of mappings in complex valued metric space and demonstrate the existence and uniqueness of the common coupled fixed points in a complete complex-valued metric space in view of diverse contractive conditions. In addition, our investigations are well supported by nontrivial examples.
Local dimensions of measures on infinitely generated self-affine sets
2014
We show the existence of the local dimension of an invariant probability measure on an infinitely generated self-affine set, for almost all translations. This implies that an ergodic probability measure is exactly dimensional. Furthermore the local dimension equals the minimum of the local Lyapunov dimension and the dimension of the space. We also give an estimate, that holds for all translation vectors, with only assuming the affine maps to be contractive.
Regression Wavelet Analysis for Lossless Coding of Remote-Sensing Data
2016
A novel wavelet-based scheme to increase coefficient independence in hyperspectral images is introduced for lossless coding. The proposed regression wavelet analysis (RWA) uses multivariate regression to exploit the relationships among wavelet-transformed components. It builds on our previous nonlinear schemes that estimate each coefficient from neighbor coefficients. Specifically, RWA performs a pyramidal estimation in the wavelet domain, thus reducing the statistical relations in the residuals and the energy of the representation compared to existing wavelet-based schemes. We propose three regression models to address the issues concerning estimation accuracy, component scalability, and c…