11856887
Approximation of linear functionals on a banach space with a Gaussian measure
Abstract We study approximation of linear functionals on separable Banach spaces equipped with a Gaussian measure. We study optimal information and optimal algorithms in average case, probabilistic, and asymptotic settings, for a general error criterion. We prove that adaptive information is not more powerful than nonadaptive information and that μ-spline algorithms, which are linear, are optimal in all three settings. Some of these results hold for approximation of linear operators. We specialize our results to the space of functions with continuous r th derivatives, equipped with a Wiener measure. In particular, we show that the natural splines of degree 2 r + I yield the optimal algorithms. We apply the general results to the problem of integration.
46374921
A Formal Specification of the ATM ABR Rate Control Scheme
Abstract Formal specifications are indispensable for computer-aided validation, verification, and testing of communication protocols. However, a large number of practical protocols, including those for ATM, have only informal English specifications. A formal specification helps in achieving a consistent interpretation and thus increases the likelihood of interoperable implementations. As a case study, we consider an important protocol — ATM's Available Bit Rate (ABR) service specification. The ABR source/destination policies have been specified using an English description in the main body of the ATM Forum's draft Traffic Management specification, from which it is hard to conduct a formal analysis. It must be noted however that considerable energy has been spent in providing a reasonably precise specification, while allowing for appropriate implementation latitude. However, an English description still has the potential for different interpretations, which may lead to discrepancy in different vendors' implementations and cause serious problems in interoperability of the communication entities made by different manufacturers. We model the ABR protocols by parameterized communicating extended finite state machines with timers, which is often called a transition system. The protocol is formally specified by the specification of the transitions of the system. We also provide insights gained in the derivation of the formal specification. Furthermore, we introduce a scheduler, involved in transmitting queued cells at the allowed cell rate to meet the minimal requirements from the source/destination protocols. We present the transitions for the source/destination/scheduler machines primarily for transmitting in-rate cells.
206832588
Optimization problems from feature testing of communication protocols
In feature testing of communication protocols, we want to construct a minimal number of tests with a desirable fault coverage. We model the protocols by extended finite state machines and reduce the test generation process to optimization problems on graphs. We study efficient algorithms and their complexity. We report experimental results on real systems, including Personal HandyPhone System, a 5ESS based ISDN wireless system, and 5ESS Intelligent Network Application Protocol.
552424
A polynomial algorithm for gateway generation from formal specifications
A systematic procedure that takes exponential time to synthesize protocol converters from formal specifications is presented. The algorithm proceeds in two steps: compute the largest common subset of services provided by the two mismatched protocols, and reduce the converter, retaining common services, without traversing the entire machine that represents the composition of the two mismatched protocols. In a number of cases, the converter can be constructed by a memoryless translation of messages from one protocol to another. Conditions under which such stateless conversion is possible are given. Two examples are presented to illustrate the techniques. In the first example, a converter that interconnects a half-duplex protocol with a full-duplex protocol from their formal specifications is computed. In the second example, the polynomial procedure is applied to computation of a converter for interconnecting the SNR and TCP protocols. >
6355860
Network Protocol System Fingerprinting - A Formal Approach
Network protocol system fingerprinting has been recognized as an important issue and a major threat to network security. Prevalent works rely largely on human experiences and insight of the protocol system specifications and implementations. Such ad-hoc approaches are inadequate in dealing with large complex protocol systems. In this paper we propose a formal approach for automated protocol system fingerprinting analysis and experiment. Parameterized Extended Finite State Machine is used to model protocol systems, and four categories of fingerprinting problems are formally defined. We propose and analyze algorithms for both active and passive fingerprinting and present our experimental results on Internet protocols. Furthermore, we investigate protection techniques against malicious fingerprinting and discuss the feasibility of two defense schemes, based on the protocol and application scenarios.
52867515
Test Sequence Selection
We study the test sequence selection problem. Given a large number of tests for a protocol system, we want to select a subset of tests so that the number of tests is reduced yet the test coverage is not sacrificed. We discuss the complexity of the test selection problem and propose a class of algorithms for different protocol system information requirements, test coverage criteria, and cost. We report experimental results on ISDN connection control protocol system Q.931.
12896882
Faster Gaussian Summation: Theory and Experiment
We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions - an O(Dp) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error control scheme integrating any arbitrary approximation method - within the best discretealgorithmic framework using adaptive hierarchical data structures. We rigorously evaluate these techniques empirically in the context of optimal bandwidth selection in kernel density estimation, revealing the strengths and weaknesses of current state-of-the-art approaches for the first time. Our results demonstrate that the new error control scheme yields improved performance, whereas the series expansion approach is only effective in low dimensions (five or less).
9084389
Restricted track assignment with applications
Consider a set of intervals S = {I1, I2, …, In}, where Ii = (li, ri), li, and ri are real numbers, and li < ri. We study a restricted track assignment problem (RTAP): if an interval Ia contains another interval Ib, then Ia must be assigned to a higher track than Ib, and the goal is to minimize the number of tracks used. The problem RTAP is shown to be NP-hard. An approximation algorithm that produces a solution within twice of the optimal is also presented and the bound is shown to be tight. The algorithm runs in O(n log n) time and requires linear space. The proposed approximation algorithm is employed to solve the problem of finding a maximum-weighted independent set in a circle graph, and related problems.
14664253
A Bit-Width Optimization Methodology for Polynomial-Based Function Evaluation
We present an automated bit-width optimization methodology for polynomial-based hardware function evaluation. Due to the analytical nature of the approach, overflow protection and precision accurate to one unit in the last place (ulp) can be guaranteed. A range analysis technique based on computing the root of the derivative of a signal is utilized to determine the minimal number of integer bits. Fractional bit requirements are established using an analytical error expression derived from the functions that occur along the data path. Global fractional bit optimization across multiple computation stages is performed using simulated annealing and circuit area estimation functions
36921568
A Study on Key Distribution and ID Registration in the AAA System for Ubiquitous Multimedia Environments
Media environment has been rapidly changed these days. Internet provides multimedia environment and has become a part of our everyday life as a new advertisement media. Authentication methods typically involve an authentication server in the home network from the authentication server of the external network, and then the external network is notified with the authentication result in the home authentication server. This paper discusses and proposes a key distribution protocol that ca be used when the user moves the external network and to ensure secure communication with the external authentication server. As the proposed technology does not receive the reissue of authentication from the home authentication server in case moving between the external authentications servers, authentication server overload can be reduced and the home network can be made to issue the key using the registered password.
42364168
An Algorithm for Incremental Nearest Neighbor Search in High-Dimensional Data Spaces
The SPY-TEC (Spherical Pyramid-Technique) [8] was proposed as a new indexing method for high-dimensional data spaces using a special partitioning strategy that divides a d-dimensional data space into 2d spherical pyramids. Although the authors of [8] proposed an efficient algorithm for processing hyperspherical range queries, they did not propose an algorithm for processing k-nearest neighbor queries that are frequently used in similarity search. In this paper, we propose an efficient algorithm for processing exact nearest neighbor queries on the SPY-TEC by extending the incremental nearest neighbor algorithm proposed in [10]. We also introduce a metric that can be used to guide an ordered best-first traversal when finding nearest neighbors on the SPYTEC. Finally, we show that our technique significantly outperforms the related techniques in processing k-nearest neighbor queries by comparing it to the R*-tree, the X-tree, and the sequential scan through extensive experiments.