9536962
On the combinatorial and algebraic complexity of quantifier elimination
In this paper, a new algorithm for performing quantifier elimination from first order formulas over real closed fields in given. This algorithm improves the complexity of the asymptotically fastest algorithm for this problem, known to this data. A new feature of this algorithm is that the role of the algebraic part (the dependence on the degrees of the imput polynomials) and the combinatorial part (the dependence on the number of polynomials) are sparated. Another new feature is that the degrees of the polynomials in the equivalent quantifier-free formula that is output, are independent of the number of input polynomials. As special cases of this algorithm new and improved algorithms for deciding a sentence in the first order theory over real closed fields, and also for solving the existential problem in the first order theory over real closed fields, are obtained.
8618090
Computing the first Betti number and the connected components of semi-algebraic sets
In this paper we describe the first singly exponential algorithm for computing the first Betti number of a given semi-algebraic set. We also describe algorithms for obtaining semi-algebraic descriptions of the semi-algebraically connected components of any given real algebraic or semi-algebraic set. Singly exponential algorithms for computing the zero-th Betti number, and the Euler-Poincaré characteristic, were known before. No singly exponential algorithm was known for computing any of the individual Betti numbers other than the zero-th one.
33624885
On the combinatorial and topological complexity of a single cell
The problem of bounding the combinatorial complexity of a single connected component (a single cell) of the complement of a set of a geometric objects in R/sup k/, each object of constant description complexity, is an important problem in computational geometry which has attracted much attention over the past decade. It has been conjectured that the combinatorial complexity of a single cell is bounded by a function much closer to O(n/sup k-1/) rather than O(n/sup k/) which is the bound for the combinatorial complexity of the whole arrangement. Till now, this was known to be rule only for k/spl les/3 and only for some special cases in higher dimensions. A classic result in real algebraic geometry due to Oleinik-Petrovsky, Thom and Milnor, bounds the topological complexity (the sum of the Betti numbers) of basic semi-algebraic sets. However, till now no better bounds were known if we restricted attention to a single connected component of a basic semi-algebraic set. In this paper, we show how these two problems are related. We prove a new bound on the sum of the Betti numbers of one connected component of a basic semi-algebraic set which is an improvement over the Oleinik-Petrovsky-Thom-Milnor bound. This also implies that the topological complexity of a single cell, measured by the sum of the Betti numbers, is bounded by O(n/sup k-1/).
24764914
Computing the Betti numbers of arrangements via spectral sequences
In this paper, we consider the problem of computing the Betti numbers of an arrangement of n compact semi-algebraic sets, S1,...,Sn ⊂ Rk, where each Si is described using a constant number of polynomials with degrees bounded by a constant. Such arrangements are ubiquitous in computational geometry. We give an algorithm for computing lth Betti number, β(∪i=1n Si), 0 ≤ l ≤ k - 1 using O(nl+2) algebraic operations. Additionally, one has to perform linear algebra on integer matrices of size bounded by O(nl+2). All previous algorithms for computing the Betti numbers of arrangements, triangulated the whole arrangement giving rise to a complex of size O(n2k) in the worst case. Thus, the complexity of computing the Betti numbers (other than the zeroth one) for these algorithms was O(n2k). To our knowledge this is the first algorithm for computing βl(∪i=1n Si) that does not rely on such a global triangulation, and has a graded complexity which depends on l.
32812813
Design of CAECC-Cellular Automata Based Error Correcting Code
A new scheme for designing error detecting and error correcting codes around cellular automata (CA) is reported. A simple and efficient scheme for generating SEC-DED codes is presented which can also be extended for generating codes with higher distances. A CA-based hardware scheme for very fast decoding (and correcting) of the codewords is also reported. >
18808745
An improved algorithm for quantifier elimination over real closed fields
We give a new algorithm for quantifier elimination in the first order theory of real closed fields that improves the complexity of the best known algorithm for this problem till now. Unlike previously known algorithms the combinatorial part of the complexity of this new algorithm is independent of the number of free variables. Moreover, under the assumption that each polynomial in the input depend only on a constant number of the free variables, the algebraic part of the complexity can also be made independent of the number of free variables. This new feature of our algorithm allows us to obtain a new algorithm for a variant of the quantifier elimination problem. We give an almost optimal algorithm for this new problem, which we call the uniform quantifier elimination problem and apply it to solve a problem arising in the field of constraint databases. No algorithm with reasonable complexity bound was known for this latter problem till now. We also point out interesting logical consequences of this algorithmic result, concerning the expressive power of a constraint query language over the reals. Moreover, our improved algorithm for performing quantifier elimination immediately leads to improved algorithms for several problems for which quantifier elimination is a basic step, for example, the problem of computing the closure of a given semi-algebraic set.
2153688
Architecture and Environment for Enabling Interactive Grids
Traditional use of grid computing allows a user to submit batch jobs in a grid environment. We believe, next generation grids will extend the application domain to include interactive graphical sessions. We term such grids Interactive Grids. In this paper, we describe some of the challenges involved in building Interactive Grids. These include fine grain access control, performance QoS guarantees, dynamic account management, scheduling, and user data management. We present the key architectural concepts in building Interactive Grids viz. hierarchical sessions, hierarchical admission control, hierarchical agents, classes of dynamic accounts, application profiling, user data management, scheduling for interactive sessions, persistent environment settings, and exporting remote desktop. We also describe IGENV, an environment for enabling interactive grids. IGENV consists of GISH –‘Grid Interactive Shell’, Controlled Desktop, SAC –‘Session Admission Control’ module, GMMA –‘Grid Monitoring and Management Agents’, and Policy Engine. We also present our testbed implementation for Interactive Grids using and extending Globus Toolkit 2.0 for the Grid middleware infrastructure, and VNC as the remote display technology.
37245904
Model checking the Java meta-locking algorithm
We apply the XMC model checker to the Java meta-locking algorithm, a highly optimized technique for ensuring mutually exclusive access by threads to object monitor queues. Our abstract specification of the meta-locking algorithm is fully parameterized, both on M, the number of threads, and N, the number of objects. Using XMC, we show that for a variety of values of M and N, the algorithm indeed provides mutual exclusion and freedom from lockout.
38040152
Multichannel permutation filters
Vector order statistic based filters designed to exploit the correlation between the channels of a multichannel signal offer improved performance over purely marginal processing. In this paper, the class of permutation filters are extended to handle multichannel signals. Permutation filters are well suited for image processing; they are robust, able to preserve details, and edges in image and video signals, and can also model complicated non-linear systems accurately. Multichannel permutation filters are based on the permutation of a set of sequential observations from a multidimensional process. There exists no unique method for the ranking of vectors, so we evaluate two ranking formulations that preserve characteristics useful in constructing estimators. Simulation results for a video restoration problem are presented.
32142802
European VAT on Digital Sales
2815801
Architecture for resource allocation services supporting interactive remote desktop sessions in utility grids
Emerging large scale utility computing systems like Grids promise computing and storage to be provided to end users as a utility. System management services deployed in the middleware are a key to enabling this vision. Utility Grids provide a challenge in terms of scale, dynamism, and heterogeneity of resources and workloads. In this paper, we present a model based architecture for resource allocation services for Utility Grids. The proposed service is built in the context of interactive remote desktop session workloads and takes application performance QoS models into consideration. The key design guidelines are hierarchical request structure, application performance models, remote desktop session performance models, site admission control, multi-variable resource assignment system, and runtime session admission control. We have also built a simulation toolkit that can handle mixed batch and remote desktop session requests, and have implemented our proposed resource allocation service into the toolkit. We present some results from experiments done using the toolkit. Our proposed architecture for resource allocation services addresses the needs of emerging utility computing systems and captures the key concepts and guidelines for building such services in these environments.