37856387
Collision-Free Communication in Sensor Networks
In this paper, we provide a stabilizing solution for collision-free diffusion in sensor networks. Such diffusions are often necessary in sensor networks when information from one sensor needs to be communicated to other sensors that satisfy certain geographic properties. Our solution deals with several difficulties, e.g., unidirectional links, unreliable links, long links, failed sensors, and sensors that are sleeping in order to save energy, that occur in sensor networks. It also ensures that there are no collisions during the diffusion and that the time required for the diffusion is O(D) where D is the diameter of the network. Moreover, while the solution can be applied to an arbitrary topology, it is more suitable for a commonly occurring topology, a two-dimensional grid. 
 
We show how our solution for collision-free diffusion can be used for time-division multiplexing (TDM) in sensor networks. TDM ensures that the message communication (other than the messages sent by diffusion) among sensors is also collision-free. While collision-free diffusion and time-division multiplexing are interdependent, we show how both these properties can be achieved simultaneously. Our algorithms are stabilizing fault-tolerant, i.e., collision-free diffusion and time-division multiplexing are restored even if the system reaches an arbitrary state where the sensors are corrupted or improperly initialized.
616074
Enhancing the fault-tolerance of nonmasking programs
In this paper we focus on automated techniques to enhance the fault-tolerance of a nonmasking fault-tolerant program to masking. A masking program continually satisfies its specification even if faults occur. By contrast, a nonmasking program merely guarantees that after faults stop occurring, the program recovers to states from where it continually satisfies its specification. Until the recovery is complete, however a nonmasking program can violate its (safety) specification. Thus, the problem of enhancing fault-tolerance from nonmasking to masking requires that safety be added and recovery be preserved. We focus on this enhancement problem for high atomicity programs-where each process can read all variables-and for distributed programs-where restrictions are imposed on what processes can read and write. We present a sound and complete algorithm for high atomicity programs and a sound algorithm for distributed programs. We also argue that our algorithms are simpler than previous algorithms, where masking fault-tolerance is added to a fault-intolerant program. Hence, these algorithms can partially reap the benefits of automation when the cost of adding masking fault-tolerance to a fault-intolerant program is high. To illustrate these algorithms, we show how the masking fault-tolerant programs for triple modular redundancy and Byzantine agreement can be obtained by enhancing the fault-tolerance of the corresponding nonmasking versions. We also discuss how the derivation of these programs is simplified when we begin with a nonmasking fault-tolerant program.
15941649
Multitolerance in Distributed Reset
A reset of a distributed system is safe if it does not complete ``prematurely,'''' i.e., without having reset some process in the system. Safe resets are possible in the presence of certain faults, such as process fail-stops and repairs, but are not always possible in the presence of more general faults, such as arbitrary transients. In this paper, we design a bounded-memory distributed-reset program that possesses two tolerances: (1) in the presence of fail-stops and repairs, it always executes resets safely, and (2) in the presence of a finite number of transient faults, it eventually executes resets safely. Designing this multitolerance in the reset program introduces the novel concern of designing a safety detector that is itself multitolerant. A broad application of our multitolerant safety detector is to make any total program likewise multitolerant.
14446337
Multitolerant Barrier Synchronization
Abstract We designed a multitolerant program for synchronizing the phases of concurrent processes. The tolerances of the program enable processes to: (i) execute all phases correctly in the presence of faults that corrupt the process state in a detectable manner, and (ii) execute only a minimum possible number of phases incorrectly before resuming correct computation in the presence of faults that corrupt the process state in an undetectable manner.
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.
38081004
A high-speed 32-bit parallel correlator for spread spectrum communication
This paper describes a high speed 32-bit pipelined digital parallel correlator implemented in a Lattice field programmable gate array (FPGA). The parallel correlator is of use in CDMA and spread spectrum transceivers for the continuous calculation of correlation between an incoming data stream with a PN sequence. The maximum frequency of operation of the FPGA based correlator is 87 MHz providing a throughput of one 32-bit correlation every 11.5 ns resulting in considerable improvement over commercially available correlators in terms of speed as well as number of bits. The high speed of operation of the correlator coupled with its ability to handle up to 32 chips per data bit alleviates the problem of low information bit rates due to signal encoding in spread spectrum communication systems. A CMOS integrated circuit implementation of the parallel correlator is presented.
14885154
On-line learning of functions of bounded variation under various sampling schemes
We consider the problem of learning of an arbitrary function selected from the non-smooth class of functions that are of bounded variation. Bounds on the prediction errors resulting from sequential type algorithms are achieved for various scenarios. It is shown that for any algorithm there exists a sequence of samples and a function that results in a unit error at each step. If the samples are i.i.d. uniform then there exists an algorithm such that for any function of bounded variation the expected error is less than O(log n/n). Furthermore, for any algorithm there exists a function such that the expected error is greater than 0(1/n). We then introduce a mixed sampling setting in which an adversary can choose points but the actual samples are drawn uniformly from a 6 neighborhood of his selection. We show that there exists an algorithm such that for any function of bounded variation and for any sequence of adversarychosen points the expected cumulative error is less than 0(+ log n). Finally, results are derived for the uniform sampling case with noisy observations. We show that the order of growth of the expected error with noise sequences in Z1 remains unaltered. However, for i.i.d. zero mean and finite variance noise there exists an algorithm with expected error less than 0(1/n*), and for i.i.d. Gaussian noise any algorithm has expected error of at least o(l/@). Permission to copy without fee all or part of this material is granted provided that the copies ars not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying IS by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. ACM COLT ’93 171931CA, USA @ 1993 Acfvf 0.89791-61 ~-5/93 /o(307/0439... $1 .50
11400186
On probably correct classification of concepts
We consider the problem of classifying an unknown concept into one of two subclasses of concepts. Specifically, if C is a concept class and Co and Cl are two disjoint subsets of C, given an unknown c E Co U Cl we wish to decide whether c c Co or c E Cl based on a set of random examples. We consider both uniform and non-uniform probably correct classification for which the number of samples is or is not required to be independent of c, respectively. For both cases, we obtain necessary and sufficient conditions on Co and Cl that allow probably correct classification. The conditions obtained are in terms of separability and/or coverability conditions on the classes Co and Cl. Furthermore, in the non-uniform case we show that this is equivalent to classification in the limit. Several examples of the applicability of our results are also provided.
1329510
Noise Conditions for Prespecified Convergence Rates of Stochastic Approximation Algorithms
We develop deterministic necessary and sufficient conditions on individual noise sequences of a stochastic approximation algorithm for the error of the iterates to converge at a given rate. Specifically, suppose {/spl rho//sub n/} is a given positive sequence converging monotonically to zero. Consider a stochastic approximation algorithm x/sub n+1/=x/sub n/-a/sub n/(A/sub n/x/sub n/-b/sub n/)+a/sub n/e/sub n/, where {x/sub n/} is the iterate sequence, {a/sub n/} is the step size sequence, {e/sub n/} is the noise sequence, and x* is the desired zero of the function f(x)=Ax-b. Then, under appropriate assumptions, we show that x/sub n/-x*=o(/spl rho//sub n/) if and only if the sequence {e/sub n/} satisfies one of five equivalent conditions. These conditions are based on well-known formulas for noise sequences: Kushner and Clark's (1978) condition, Chen's (see Proc. IFAC World Congr., p.375-80, 1996) condition, Kulkarni and Horn's (see IEEE Trails Automat. Contr., vol.41, p.419-24, 1996) condition, a decomposition condition, and a weighted averaging condition. Our necessary and sufficient condition on {e/sub n/} to achieve a convergence rate of {/spl rho//sub n/} is basically that the sequence {e/sub n///spl rho//sub n/} satisfies any one of the above five well-known conditions. We provide examples to illustrate our result. In particular, we easily recover the familiar result that if a/sub n/=a/n and {e/sub n/} is a martingale difference process with bounded variance, then x/sub n/-x*=o(n/sup -1/2/(log(n))/sup /spl beta//) for any /spl beta/>1/2.
7360646
Upper bounds to transport capacity of wireless networks
We derive upper bounds on the transport capacity of wireless networks. The bounds obtained are solely dependent on the geographic locations and power constraints of the nodes. As a result of this derivation, we are able to conclude the optimality, in the sense of scaling of transport capacity with the number of nodes, of a multihop communication strategy for a class of network topologies.