5215725
Linear Complexity versus Pseudorandomness: On Beth and Dai's Result
Beth and Dai studied in their Eurocrypt paper [1] the relationship between linear complexity (that is, the length of the shortest Linear Feedback Shift Register that generates the given strings) of strings and the Kolmogorov complexity of strings. Though their results are correct, some of their proofs are incorrect. In this note, we demonstrate with a counterexample the reason why their proofs are incorrect and we prove a stronger result. We conclude our note with some comments on the use of the LIL test (the law of the iterated logarithm) for pseudorandom bits generated by pseudorandom generators.
8968053
Resource-Bounded Balanced Genericity, Stochasticity and Weak Randomness
We introduce balanced t(n)-genericity which is a refinement of the genericity concept of Ambos-Spies, Fleischhack and Huwig [2] and which in addition controls the frequency with which a condition is met. We show that this concept coincides with the resource-bounded version of Church's stochasticity [6]. By uniformly describing these concepts and weaker notions of stochasticity introduced by Wilber [19] and Ko [11] in terms of prediction functions, we clarify the relations among these resource-bounded stochasticity concepts. Moreover, we give descriptions of these concepts in the framework of Lutz's resource-bounded measure theory [13] based on martingales: We show that t(n)-stochasticity coincides with a weak notion of t(n)-randomness based on so-called simple martingales but that it is strictly weaker than t(n)-randomness in the sense of Lutz.
41292415
Randomness, Stochasticity and Approximations
Polynomial time unsafe approximations for intractable sets were introduced by Meyer and Paterson [9] and Yesha [19], respectively. The question of which sets have optimal unsafe approximations has been investigated extensively; see, e.g., [1], [5], [15], and [17]. Recently, Wang [15], [17] showed that polynomial time random sets are neither optimally unsafe approximable nor Δ -levelable. In this paper we show that: (1) There exists a polynomial time stochastic set in the exponential time complexity class which has an optimal unsafe approximation. (2) There exists a polynomial time stochastic set in the exponential time complexity class which is Δ -levelable. The above two results answer a question asked by Ambos-Spies and Lutz [2]: What kind of natural complexity property can be characterized by p -randomness but not by p -stochasticity? Our above results also extend Ville's [13] historical result. The proof of our first result shows that, for Ville's stochastic sequence, we can find an optimal prediction function f such that we will never lose our own money betting according to f (except the money we have earned), that is to say, if at the beginning we have only $1 and we always bet $1 that the next selected bit is 1 , then we always have enough money to bet on the next bit. Our second result shows that there is a stochastic sequence for which there is a betting strategy f such that we will never lose our own money betting according to f (except the money we have earned), but there is no such optimal betting strategy. That is to say, for any such betting strategy, we can find another betting strategy which could be used to make money more quickly.
10131509
Using Approximation Hardness to Achieve Dependable Computation
Redundancy has been utilized to achieve fault tolerant computation and to achieve reliable communication in networks of processors. These techniques can only be extended to computations solely based on functions in one input in which redundant hardware or software (servers) are used to compute intermediate and end results. However, almost all practical computation systems consist of components which are based on computations with multiple inputs. Wang, Desmedt, and Burmester have used AND/OR graphs to model this scenario. Roughly speaking, an AND/OR graph is a directed graph with two types of vertices, labeled ∧-vertices and ∨-vertices. In this case, processors which need all their inputs in order to operate could be represented by ∧-vertices, whereas processors which can choose one of their "redundant" inputs could be represented by ∨-vertices. In this paper, using the results for hardness of approximation and optimization problems, we will design dependable computation systems which could defeat as many malicious faults as possible. Specifically, assuming certain approximation hardness result, we will construct k-connected AND/OR graphs which could defeat a ck-active adversary (therefore a ck-passive adversary also) where c > 1 is any given constant. This result improves a great deal on the results for the equivalent communication problems.
8247434
NP-Hard Sets are Superterse Unless NP is Small
Abstract We show that the class P- mc ( n ) of polynomial time n -membership comparable sets (defined by Ogihara, 1995) has p -measure 0. Using this result, we will show that the class of sets which are ⩽ tt P -reducible to some P-selective set has p -measure 0. Furthermore, we will show that if NP does not have p -measure 0 then no ⩽ tt p -hard set for NP is P-approximable.
5135938
Privacy preserving database application testing
Traditionally, application software developers carry out their tests on their own local development databases. However, such local databases usually have only a small number of sample data and hence cannot simulate satisfactorily a live environment, especially in terms of performance and scalability testing. On the other hand, the idea of testing applications over live production databases is increasingly problematic in most situations primarily due to the fact that such use of live production databases has the potential to expose sensitive data to an unauthorized tester and to incorrectly update information in the underlying database. In this paper, we investigate techniques to generate mock databases for application software testing without revealing any confidential information from the live production databases. Specifically, we will design mechanisms to create the deterministic rule set R, non-deterministic rule set N R, and statistic data set S for a live production database. We will then build a security Analyzer which will process the triplet <R',N R',S'> together with security requirements (security policy) and output a new triplet <R',N R',S'> The security Analyzer will guarantee that no confidential information could be inferred from the new triplet <R',N R',S'> The mock database generated from this new triplet can simulate the live environment for testing purpose, while maintaining the privacy of data in the original database.
40360434
Measurement of the cognitive functional complexity of software
One of the central problems in software engineering is its inherited complexity. It is recognized that cognitive informatics plays an important role in understanding the fundamental characteristics of software. This paper models the cognitive weights of basic control structures of software, and develops a new concept of cognitive functional size for measuring software complexity. Comparative case studies between the cognitive functional size and physical sizes of 20 programs are conducted. It is found that for a given design, although the physical sizes of software may vary in a wide range, the cognitive functional sizes are much stable and independent from implementation technologies and programming languages. Therefore, the cognitive functional size provides a novel, stable and practical software complexity measurement and is helpful to explain the fundamental nature of software complexity in the phase of design, implementation, or maintenance in software engineering.
1235699
High resolution tracking of non-rigid 3D motion of densely sampled data using harmonic maps
We present a novel fully automatic method for high resolution, nonrigid dense 3D point tracking. High quality dense point clouds of nonrigid geometry moving at video speeds are acquired using a phase-shifting structured light ranging technique. To use such data for the temporal study of subtle motions such as those seen in facial expressions, an efficient nonrigid 3D motion tracking algorithm is needed to establish inter-frame correspondences. The novelty of this paper is the development of an algorithmic framework for 3D tracking that unifies tracking of intensity and geometric features, using harmonic maps with added feature correspondence constraints. While the previous uses of harmonic maps provided only global alignment, the proposed introduction of interior feature constraints guarantees that nonrigid deformations are accurately tracked as well. The harmonic map between two topological disks is a diffeomorphism with minimal stretching energy and bounded angle distortion. The map is stable, insensitive to resolution changes and is robust to noise. Due to the strong implicit and explicit smoothness constraints imposed by the algorithm and the high-resolution data, the resulting registration/deformation field is smooth, continuous and gives dense one-to-one inter-frame correspondences. Our method is validated through a series of experiments demonstrating its accuracy and efficiency.
7330330
Steganalysis of block-structured stegotext
We study a detection-theoretic approach to steganalysis. The relative entropy between covertext and stegotext determines the steganalyzer's difficulty in discriminating them, which in turn defines the detectability of the stegosystem. We consider the case of Gaussian random covertexts and mean-squared embedding constraint. We derive a lower bound on the relative entropy between covertext and stegotext for block-based embedding functions. This lower bound can be approached arbitrarily closely using a spread-spectrum method and secret keys with large entropy. The lower bound can also be attained using a stochastic quantization index modulation (QIM) encoder, without need for secret keys. In general, perfect undetectability can be achieved for blockwise memoryless Gaussian covertexts. For general Gaussian covertexts with memory, the relative entropy increases approximately linearly with the number of blocks observed by the steganalyzer. The error probabilities of the best steganalysis methods decrease exponentially with the number of blocks.
1078542
Energy-efficient computing for wildlife tracking: design tradeoffs and early experiences with ZebraNet
Over the past decade, mobile computing and wireless communication have become increasingly important drivers of many new computing applications. The field of wireless sensor networks particularly focuses on applications involving autonomous use of compute, sensing, and wireless communication devices for both scientific and commercial purposes. This paper examines the research decisions and design tradeoffs that arise when applying wireless peer-to-peer networking techniques in a mobile sensor network designed to support wildlife tracking for biology research.The ZebraNet system includes custom tracking collars (nodes) carried by animals under study across a large, wild area; the collars operate as a peer-to-peer network to deliver logged data back to researchers. The collars include global positioning system (GPS), Flash memory, wireless transceivers, and a small CPU; essentially each node is a small, wireless computing device. Since there is no cellular service or broadcast communication covering the region where animals are studied, ad hoc, peer-to-peer routing is needed. Although numerous ad hoc protocols exist, additional challenges arise because the researchers themselves are mobile and thus there is no fixed base station towards which to aim data. Overall, our goal is to use the least energy, storage, and other resources necessary to maintain a reliable system with a very high `data homing' success rate. We plan to deploy a 30-node ZebraNet system at the Mpala Research Centre in central Kenya. More broadly, we believe that the domain-centric protocols and energy tradeoffs presented here for ZebraNet will have general applicability in other wireless and sensor applications.
1878790
Unsupervised Discovery of Action Classes
In this paper we consider the problem of describing the action being performed by human figures in still images. We will attack this problem using an unsupervised learning approach, attempting to discover the set of action classes present in a large collection of training images. These action classes will then be used to label test images. Our approach uses the coarse shape of the human figures to match pairs of images. The distance between a pair of images is computed using a linear programming relaxation technique. This is a computationally expensive process, and we employ a fast pruning method to enable its use on a large collection of images. Spectral clustering is then performed using the resulting distances. We present clustering and image labeling results on a variety of datasets.