47390024
On the combinatorial and algebraic complexity of quantifier elimination
In this paper we give a new algorithm for performing quantifier elimination from first order formulae over real closed fields. This algorithm improves the complexity of the asymptotically fastest algorithm for this problem, known to this date. A new feature of our algorithm is that the role of the algebraic part (the dependence on the degrees of the input polynomials) and the combinatorial part (the dependence on the number of polynomials) are separated, making possible our improved complexity bound. Another new feature is that the degrees of the polynomials in the equivalent quantifier-free formula that we output, are independent of the number of input polynomials. As special cases of this algorithm, we obtain 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. Using the theory developed in this paper, we also give an improved bound on the radius of a ball centered at the origin, which is guaranteed to intersect every connected component of the sign partition induced by a family of polynomials. We also use our methods to obtain algorithms for solving certain decision problems in real and complex geometry which improves the complexity of the currently known algorithms for these problems.<<ETX>>
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.
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.
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. >
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.
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.
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.
16902988
A Cost-Sensitive Model for Preemptive Intrusion Response Systems
The proliferation of complex and fast-spreading intrusions not only requires advances in intrusion detection mechanisms but also demands development of sophisticated and automated intrusion response systems. In this paper we present a novel cost-sensitive model for intrusion response that incorporates preemptive deployment of the response actions. Specifically, our technique relies on comparing the cost of deploying a response against the cost of damage caused by an "'un-attended" intrusion and decides to preemptively deploy a response with maximum benefit. Our technique further allows adaptation of responses to the changing environment through evaluation of success and failure of previously triggered responses. We demonstrate the advantages of the approach and evaluate it using a damage reduction metric.
9474380
3D Modeling of Human Lip Motion
908197
WebSob: A Tool for Robustness Testing of Web Services
Web services are a popular way of implementing a service-oriented architecture. Testing can be used to help assure both the correctness and robustness of a web service. Because manual testing is tedious, tools are needed to automate test generation and execution for web services. This paper presents WebSob, a tool for automatically generating and executing web-service requests given a service provider's Web service description language (WSDL) specification. We have applied WebSob to freely available web services and our experiences show that WebSob can be used to quickly generate and execute web-service requests that may reveal robustness problems with no knowledge of the underlying web service implementation.