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threshold computation and cryptographic security

SIAM JOURNAL ON COMPUTING 1997年第1期26卷 59-78页

作者： Han, YN Hemaspaandra, LA Thierauf, T UNIV ROCHESTER DEPT COMP SCI ROCHESTER NY 14627 USA UNIV ULM ABT THEORET INFORMAT D-89069 ULM GERMANY PRINCETON UNIV PRINCETON NJ 08544 USA

threshold machines are Turing machines whose acceptance is determined by what portion of the machine's computation paths are accepting paths. Probabilistic machines are Turing machines whose acceptance is determined by the probability weight of the machine's accepting computation paths. In 1975, Simon proved that for unbounded-error polynomial-time machines these two notions yield the same class, PP. Perhaps because Simon's result seemed to collapse the threshold and probabilistic modes of computation, the relationship between threshold and probabilistic computing for the case of bounded error has remained unexplored. In this paper, we compare the bounded-error probabilistic class BPP with the analogous threshold class, BPPpath, and, more generally, we study the structural properties of BPPpath. We prove that BPPpath contains both NPBPP and P-NP[log] and that BPPpath is contained in P-Sigma 2p[log], BPPNP, and PP. We conclude that, unless the polynomial hierarchy collapses, bounded-error threshold computation is strictly more powerful than bounded-error probabilistic computation. We also consider the natural notion of secure access to a database: an adversary who watches the queries should gain no information about the input other than perhaps its length. We show for both BPP and BPPpath that if there is a ny database for which this formalization of security differs from the security given by oblivious database access, then P not equal PSPACE. It follows that if any set lacking small circuits can be securely accepted, then P not equal PSPACE.

关键词： complexity theory cryptography probabilistic computation threshold computation

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threshold computation for fault detection in linear discrete-time Markov jump systems

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INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING 2014年第11期28卷 1106-1127页

作者： Saijai, Jedsada Ding, Steven X. Abdo, Ali Shen, Bo Damlakhi, Waseem Univ Duisburg Essen Inst Automat Control & Complex Syst AKS Fac Engn D-47057 Duisburg Germany

This paper proposes a threshold computation scheme for an observer-based fault detection (FD) in linear discrete-time Markovian jump systems. An observer-based FD scheme typically consists of two stages known as residual generation and residual evaluation. Even information of faults is contained inside a residual signal, a decision of faults occurrence is consequently made by a residual evaluation stage, which consists of residual evaluation function and threshold setting. For this reason, a successful FD strongly depends on a threshold setting for a given residual evaluation function. In this paper, Kalman filter (KF) is used as a residual generator. Based on an accessibility of Markov chain to KF, two types of residual generations are considered, namely mode-dependent and mode-independent residual generation. After that threshold is computed in a residual evaluation stage such that a maximum fault detection rate is achieved, for a given false alarm rate. Without any knowledge of a probability density function of residual signal before and after fault occurrence, a threshold is computed by using an estimation of residual evaluation function variance in a fault-free case. Finally, a detection performance is demonstrated by a numerical example. Copyright (c) 2013 John Wiley & Sons, Ltd.

关键词： fault detection linear Markov jump systems Markov chain residual evaluation threshold computation

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Dynamic threshold computation in fault detection for discrete-time linear systems 30

Dynamic threshold computation in fault detection for discret...

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30th Chinese Control and Decision Conference (CCDC)

作者： Liu, Xinyang Wang, Zhenhua Wang, Ye Shen, Yi Harbin Inst Technol Sch Astronaut Harbin 150001 Peoples R China Univ Politecn Catalunya BarcelonaTech UPC Inst Robot & Informat Ind CSIC UPC C Llorens & Artigas 4-6 Barcelona 08028 Spain

ISBN: (纸本)9781538612446

This paper studies threshold computation in observer-based fault detection for discrete-time linear systems subject to unknown but bounded uncertainties. Based on two different assumptions on uncertainties, we propose two threshold computation methods for residual evaluation. First, we assume that the uncertainties are bounded in known intervals and propose a zonotope-based threshold computation method. Second, the uncertainties are assumed to be norm-bounded and then a threshold computation method using L-infinity analysis is proposed. Numerical simulations are given to verify and compare the performance of the proposed methods.

关键词： Fault detection threshold computation Zonotopes L-infinity analysis

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Dynamic threshold computation in fault detection for discrete-time linear systems

Dynamic threshold computation in fault detection for discret...

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第30届中国控制与决策会议

作者： Xinyang Liu Zhenhua Wang Ye Wang Yi Shen School of Astronautics Harbin Institute of Technology Institut de Robòtica i Informatica Industrial CSIC-UPC Universitat Politècnica de Catalunya-BarcelonaTech (UPC)

This paper studies threshold computation in observer-based fault detection for discrete-time linear systems subject to unknown but bounded uncertainties. Based on two different assumptions on uncertainties, we propose two threshold computation methods for residual evaluation. First, we assume that the uncertainties are bounded in known intervals and propose a zonotope-based threshold computation method. Second, the uncertainties are assumed to be norm-bounded and then a threshold computation method using L∞ analysis is proposed. Numerical simulations are given to verify and compare the performance of the proposed methods.

关键词： Fault detection threshold computation Zonotopes L∞ analysis

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Fuzzy linguistic logic programming and its applications

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THEORY AND PRACTICE OF LOGIC PROGRAMMING 2009年第3期9卷 309-341页

作者： Le, Van Hung Liu, Fei Tran, Dinh Khang La Trobe Univ Dept Comp Sci & Comp Engn Bundoora Vic 3086 Australia Hanoi Univ Technol Fac Informat Technol Hanoi Vietnam

The paper introduces FUZZY linguistic logic programming, which is a combination of fuzzy logic programming, introduced by P. Vojtas, and hedge algebras in order to facilitate the representation and reasoning on human knowledge expressed in natural languages. In fuzzy linguistic logic programming, truth values are linguistic ones, e.g., Very True, Very Probably True and Little False, taken from a hedge algebra of a linguistic truth variable, and linguistic hedges (modifiers) can be used as unary connectives in formulae. This is motivated by the fact that humans reason mostly in terms of linguistic terms rather than in terms of numbers, and linguistic hedges are often used in natural languages to express different levels of emphasis. The paper presents: (a) the language Of fuzzy linguistic logic programming;(b) a declarative semantics in terms of Herbrand interpretations and models;(c) a procedural semantics which directly manipulates linguistic terms to Compute a lower bound to the truth Value of a query, and proves its soundness;(d) a fixpoint semantics of logic programs, and based on it, proves the completeness of the procedural semantics;(e) several applications of fuzzy linguistic logic programming;and (f) an idea of implementing a system to execute fuzzy linguistic logic programs.

关键词： fuzzy logic programming hedge algebra linguistic value linguistic hedge computing with words databases querying threshold computation fuzzy control

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Analysis of the iterative decoding of LDPC and product codes using the Gaussian approximation

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IEEE TRANSACTIONS ON INFORMATION THEORY 2003年第11期49卷 2993-3000页

作者： Lehmann, F Maggio, GM CNRS LAAS F-31077 Toulouse France STMicroelect Inc Adv Syst Technol San Diego CA USA Univ Calif San Diego Ctr Wireless Commun La Jolla CA 92093 USA

We propose a novel density evolution approach to analyze the iterative decoding algorithms of low-density parity-check (LDPC) codes and product codes, based on Gaussian densities. Namely, for these classes of codes we derive a one-dimensional (I-D) map whose iterates directly represent the error probability both for the additive white Gaussian noise (AWGN) and the Rayleigh-fading channel. These simple models allow a qualitative analysis of the nonlinear dynamics of the decoding algorithm. As an application, we compute the decoding thresholds and show that they are consistent with the simulation results available in the literature.

关键词： density evolution Gaussian approximation low-density parity-check (LDPC) codes nonlinear dynamics threshold computation

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An efficient approach to compute the threshold for multi-dimensional linear classifiers

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PATTERN RECOGNITION 2004年第4期37卷 811-826页

作者： Rueda, L Univ Windsor Sch Comp Sci Windsor ON N9B 3P4 Canada

In this paper, we theoretically analyze some properties that relate Fisher's classifier and the optimal quadratic classifier, when the latter is derived utilizing a particular covariance matrix for the classes. We propose an efficient approach which is used to select the threshold after a linear transformation onto the one-dimensional space is performed. We achieve this by selecting the decision boundary that minimizes the classification error in the transformed space, assuming that the univariate random variables are normally distributed. Our empirical results on synthetic and real-life data sets show that our approach lead to smaller classification error than the traditional Fisher's classifier. The results also demonstrate that minimizing the classification error in the transformed space leads to smaller classification error in the original multi-dimensional space. (C) 2003 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.

关键词： linear classifiers normally distributed classes Fisher's classifier threshold computation error evaluation

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threshold dominating sets and an improved characterization of W

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THEORETICAL COMPUTER SCIENCE 1998年第1-2期209卷 123-140页

作者： Downey, RG Fellows, MR Univ Victoria Dept Math Wellington New Zealand Univ Victoria Dept Comp Sci Victoria BC V8W 3P6 Canada

The threshold DOMINATING SET problem is that of determining for a graph G = (V,E) whether there is a subset V' subset of or equal to V of size k, such that for each vertex v is an element of V there are at least r elements of the closed neighborhood N[v] that belong to V'. We consider the complexity of the problem parameterized by the pair (k,r). It is trivial to observe that this is hard for W[2]. It can also be easily shown to belong to a natural extension W*[2] of W[2] defined in terms of circuit families of depth bounded by a function of the parameter. We prove membership in W[2] and thus W[2]-completeness. Using this as a starting point, we prove that W*[2] = W[2]. (C) 1998-Elsevier Science B.V. All rights reserved.

关键词： parameterized complexity dominating sets threshold computation satisfiability problems Boolean circuits

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Tabulation proof procedures for fuzzy linguistic logic programming

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INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 2015年 63卷 62-88页

作者： Van Hung Le Liu, Fei Hanoi Univ Min & Geol Fac Informat Technol Hanoi Vietnam La Trobe Univ Dept Comp Sci & Comp Engn Bundoora Vic 3086 Australia

Fuzzy linguistic logic programming is a logical system for representing and reasoning with linguistically-expressed human knowledge. In fuzzy linguistic logic programming, up until now, there have been only two methods to compute answers to a query w.r.t. a logic program: (i) by bottom-up iterating the immediate consequence operator T-p;or (ii) by using the procedural semantics. Nevertheless, the former is exhaustive and not goal-oriented. Indeed, it requires computation of the whole least Herbrand model despite the fact that not all the results are required to determine the answer of the query. On the other hand, although the latter is goal-oriented, it may lead to an infinite loop and may recompute atoms in rule bodies. Furthermore, it may not, in general, give a most general answer to a query. In this paper, we develop two query answering procedures which can overcome these problems for fuzzy linguistic logic programming. More precisely, the non-deterministic tabulation procedure is close to the procedural semantics and gives all answers to a query. The deterministic tabulation procedure is more efficient than the non-deterministic one and gives all and only the most general answers to a query. The deterministic procedure also enables threshold computation and top-k retrieval. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Fuzzy logic programming Tabulation proof procedure Linguistic truth value Hedge connective threshold computation Top-k retrieval

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Isolating Misbehaving Nodes in MANETs with an Adaptive Trust threshold Strategy

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MOBILE NETWORKS & APPLICATIONS 2017年第3期22卷 493-509页

作者： Khan, Muhammad Saleem Midi, Daniele Malik, Saif-Ur-Rehman Khan, Majid I. Javaid, Nadeem Bertino, Elisa COMSATS Inst Informat Technol Dept Comp Sci Islamabad Pakistan Purdue Univ Dept Comp Sci W Lafayette IN 47907 USA

Due to dynamic network topology, distributed architecture and absence of a centralized authority, Mobile Ad hoc Networks (MANETs) are vulnerable to various attacks from misbehaving nodes. To enhance the security of MANETs, various trust-based schemes have been proposed that augment the traditional cryptography-based security schemes. However, most of these schemes use static and predefined trust thresholds for node misbehavior detection, without taking into consideration the network conditions locally at each node. Using static trust thresholds for misbehavior detection may result in high false positives, low malicious node detection rate, and network partitioning. In this paper, we propose a novel Adaptive Trust threshold (ATT) strategy that adapts the trust threshold in the routing protocol according to the network conditions such as rate of link changes, node degree and connectivity, and average neighborhood trustworthiness. We identify the topology factors that affect the trust threshold at each node, and leverage them to build a mathematical model for ATT computation. We compare our ATT strategy with one of the most recently proposed trust-based security schemes. Our simulation results indicate that the ATT strategy is robust in terms of convergence to the same trust threshold value computed at all neighbor nodes for malicious nodes and is energy efficient. Moreover, the ATT strategy achieves significant improvements in packet delivery ratio, reduction in false positives, and increase in detection rate as compared to non-ATT schemes (static trust threshold based schemes).

关键词： MANETs threshold computation Adaptive threshold Static threshold Colluding attackers

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