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.
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.
10508326
The Combinatorial and Topological Complexity of a Single Cell 


Abstract. The problem of bounding the combinatorial complexity of a single connected component (a single cell) of the complement of a set of n geometric objects in Rk, 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(nk-1) rather than O(nk) which is the bound for the combinatorial complexity of the whole arrangement. Until now, this was known to be true only for k ≤ 3 and only for some special cases in higher dimensions. A classic result in real algebraic geometry due to Oleinik and Petrovsky [15], Thom [18], and Milnor [14], bounds the topological complexity (the sum of the Betti numbers) of basic semi-algebraic sets. However, until 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(nk-1) . The techniques used for proving this topological result combined with those developed by Halperin and Sharir for the single cell problem in three dimensions allow us to prove a bound of O(nk-1+ε) on the combinatorial complexity of a single cell. Finally, we show that under a certain natural geometric assumption on the objects (namely, that whenever they intersect, the intersection is robustly transversal) it is possible to prove a bound of O(nk-1) on the combinatorial complexity of a single cell. 

75418
Combinatorial complexity in O-minimal geometry
In this paper we prove tight bounds on the combinatorial and topological complexity of sets dened in terms of n denable sets belonging to some fixed denable family of sets in an o-minimal structure. This generalizes the combinatorial parts of similar bounds known in the case of semi-algebraic and semi-Pfaffian sets, and as a result vastly increases the applicability of results on combinatorial and topological complexity of arrangements studied in discrete and computational geometry. As a sample application, we extend a Ramsey-type theorem due to Alon et al. [3], originally proved for semi-algebraic sets of fixed description complexity to this more general setting.
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. >
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/).
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.
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.
6329098
Web Service Dependency Discovery Tool for SOA Management
In this paper we identify the importance of the problem of discovering dynamic dependencies among Web services. The approach we take is to automate the identification of traces of dependent messages, based on the correlation of messages exchanged among services. We infer service dependencies based on the correlated message traces.
121785
Generation of All Counter-Examples for Push-Down Systems
We present a new, on-the-fly algorithm that given a push-down model representing a sequential program with (recursive) procedure calls and an extended finite-state automaton representing (the negation of) a safety property, produces a succinct, symbolic representation of all counter-examples; i.e., traces of system behaviors that violate the property. The class of what we call minimum-recursion loop-free counter-examples can then be generated from this representation on an as-needed basis and presented to the user. Our algorithm is also applicable, without modification, to finite-state system models. Simultaneous consideration of multiple counter-examples can minimize the number of model-checking runs needed to recognize common root causes of property violations. We illustrate the use of our techniques via application to a Java-Tar utility and an FTP-server program, and discuss a prototype tool implementation which offers several abstraction techniques for easy-viewing of generated counter-examples.
17954434
Fast proxy delivery of multiple streaming sessions in shared running buffers
With the falling price of memory, an increasing number of multimedia servers and proxies are now equipped with a large memory space. Caching media objects in the memory of a proxy helps to reduce the network traffic, the disk I/O bandwidth requirement, and the data delivery latency. The running buffer approach and its alternatives are representative techniques to caching streaming data in the memory. There are two limits in the existing techniques. First, although multiple running buffers for the same media object co-exist in a given processing period, data sharing among multiple buffers is not considered. Second, user access patterns are not insightfully considered in the buffer management. In this paper, we propose two techniques based on shared running buffers in the proxy to address these limits. Considering user access patterns and characteristics of the requested media objects, our techniques adaptively allocate memory buffers to fully utilize the currently buffered data of streaming sessions, with the aim to reduce both the server load and the network traffic. Experimentally comparing with several existing techniques, we show that the proposed techniques achieve significant performance improvement by effectively using the shared running buffers.