6063474
PAC learning with generalized samples and an application to stochastic geometry
In this paper, we introduce an extension of the standard PAC learning model which allows the use of generalized samples. We view a generalized sample as a pair consisting of a functional on the concept class together with the value obtained by the functional operating on the unknown concept. It appears that this model can be applied to a number of problems in signal processing and geometric reconstruction to provide sample size bounds under a PAC criterion. We consider a specific application of the model to a problem of curve reconstruction, and discuss some connections with a result from stochastic geometry.
2831656
Universal coding of nonstationary sources
We investigate the performance of the Lempel-Ziv (1978) incremental parsing scheme on nonstationary sources. We show that it achieves the best rate achievable by a finite-state block coder for the nonstationary source. We also show a similar result for a lossy coding scheme given by Yang and Kieffer (see ibid., vol.42, p.239-45, 1996) which uses a Lempel-Ziv scheme to perform lossy coding.
2812660
Local Versus Non-local Computation of Length of Digitized Curves
We consider the problem of computing the length of a curve from digitized versions of the curve using parallel computation. Our aim is to study the inherent parallel computational complexity of this problem as a function of the digitization level. Precise formulations for the digitization, the parallel computation, and notions of local and nonlocal computations are given. We show that length cannot be computed locally from digitizations on rectangular tessellations. However, for a random tessellation and appropriate deterministic ones, we show that the length of straight line segments can be computed locally.
53223319
Learning Changing Concepts by Exploiting the Structure of Change
This paper examines learning problems in which the target function is allowed to change. The learner sees a sequence of random examples, labelled according to a sequence of functions, and must provide an accurate estimate of the target function sequence. We consider a variety of restrictions on how the target function is allowed to change, including infrequent but arbitrary changes, sequences that correspond to slow walks on a graph whose nodes are functions, and changes that are small on average, as measured by the probability of disagreements between consecutive functions. We first study estimation, in which the learner sees a batch of examples and is then required to give an accurate estimate of the function sequence. Our results provide bounds on the sample complexity and allowable drift rate for these problems. We also study prediction, in which the learner must produce online a hypothesis after each labelled example and the average misclassification probability over this hypothesis sequence should be small. Using a deterministic analysis in a general metric space setting, we provide a technique for constructing a successful prediction algorithm, given a successful estimation algorithm. This leads to sample complexity and drift rate bounds for the prediction of changing concepts.
15102047
Separation of random number generation and resolvability
We consider the problem of determining when a given source can be used to approximate the output due to any input to a given channel. We provide achievability and converse results for a general source and channel. For the special case of a full-rank discrete memoryless channel we give a stronger converse result than we can give for a general channel.
15475360
Estimating correspondence in digital video
This paper addresses several estimation problems involving correspondence in digital video. We present three cases, in order of increasing complexity: affine transformations, projective transformations, and general correspondence. We review some recent research in the first two cases and present a new framework for discussing the third case. We also discuss how to use the formalism of correspondence graphs to ensure that any estimated correspondence is physically valid.
442686
The effect of the specification model on the complexity of adding masking fault tolerance
In this paper, we investigate the effect of the representation of safety specification on the complexity of adding masking fault tolerance to programs - where, in the presence of faults, the program 1) recovers to states from where it satisfies its (safety and liveness) specification and 2) preserves its safety specification during recovery. Specifically, we concentrate on two approaches for modeling the safety specifications: 1) the bad transition (BT) model, where safety is modeled as a set of bad transitions that should not be executed by the program, and 2) the bad pair (BP) model, where safety is modeled as a set of finite sequences consisting of at most two successive transitions. If the safety specification is specified in the BT model, then it is known that the complexity of automatic addition of masking fault tolerance to high atomicity programs - where processes can read/write all program variables in an atomic step) - is polynomial in the state space of the program. However, for the case where one uses the BP model to specify safety specification, we show that the problem of adding masking fault tolerance to high atomicity programs is NP-complete. Therefore, we argue that automated synthesis of fault-tolerant programs is likely to be more successful if one focuses on problems where safety can be represented in the BT model.
2979288
Transformations for write-all-with-collision model,
Dependable properties such as self-stabilization are crucial requirements in sensor networks. One way to achieve these properties is to utilize the vast literature on distributed systems where such self-stabilizing algorithms have been designed. Since these existing algorithms are designed in read/write model (or variations thereof), they cannot be directly applied in sensor networks. For this reason, we consider a new atomicity model, write all with collision (WAC), that captures the computations of sensor networks and focus on transformations from read/write model to WAC model and vice versa. We show that the transformation from WAC model to read/write model is stabilization preserving, and the transformation from read/write model to WAC model is stabilization preserving for timed systems. In the transformation from read/write model to WAC model, if the system is untimed (asynchronous) and processes are deterministic then under reasonable assumptions, we show that (1) the resulting program in WAC model can allow at most one process to execute, and (2) the resulting program in WAC model cannot be stabilizing.
6871855
The complexity of adding failsafe fault-tolerance
In this paper, we focus our attention on the problem of automating the addition of failsafe fault-tolerance where fault-tolerance is added to an existing (fault-intolerant) program. A failsafe fault-tolerant program satisfies its specification (including safety and liveness) in the absence of faults. And, in the presence of faults, it satisfies its safety specification. We present a somewhat unexpected result that, in general, the problem of adding failsafe fault-tolerance in distributed programs is NP-hard. Towards this end, we reduce the 3-SAT problem to the problem of adding failsafe fault-tolerance. We also identify a class of specifications, monotonic specifications and a class of programs, monotonic programs. Given a (positive) monotonic specification and a (negative) monotonic program, we show that failsafe fault-tolerance can be added in polynomial time. We note that the monotonicity restrictions are met for commonly encountered problems such as Byzantine agreement, distributed consensus, and atomic commitment. Finally, we argue that the restrictions on the specifications and programs are necessary to add failsafe fault-tolerance in polynomial time; we prove that if only one of these conditions is satisfied, the addition of failsafe fault-tolerance is still NP-hard.
12683811
Proactive Reliable Bulk Data Dissemination in Sensor Networks
One of the problems in network reprogramming is to guarantee 100 percent delivery of a large amount of data (the entire binary image) in a lossy wireless channel. All the existing protocols on network reprogramming [1–6] use automatic repeat request (ARQ) scheme to recover from packet losses. We propose a new reliability scheme which is a hybrid approach of forward error correction (FEC) and ARQ. We perform a case study on MNP, a multihop network reprogramming protocol, and study the effect of adding two different FEC codes: simple XOR code and Reed-Solomon (RS) codes [7], to MNP. We evaluate the new reliability approach using TOSSIM. The simulation results show that adding simple XOR code to MNP can achieve up to 10% improvement on reprogramming speed and up to 18% reduction on active radio time (the major part of energy consumption). And we show that RS codes perform even better.
14751317
Reducing the cost of the critical path in secure multicast for dynamic groups
In this paper we focus on the problem of secure multicast in dynamic groups. In this problem, a group of users communicate using a shared key. Due to the dynamic nature of these groups, to preserve secrecy, it is necessary to change the group key whenever the group membership changes. While the group key, is being changed, the group communication needs to be interrupted until the rekeying is complete. This interruption is especially necessary if the rekeying is done because a user has left (or is removed). We split the rekeying cost into two parts: the cost of the critical path-where each user receives the new group key, and the cost of the non-critical path-where each user receives any other keys that it needs to obtain. We present two algorithms that show the trade off between the cost of the critical path and the cost of the non-critical path. We also compare our algorithms to previous algorithms and show that our algorithms reduce the cost of the critical path while keeping the total cost manageable.