Joseph Y. Halpern, Nimrod Megiddo, and Ashfaq A. Munshi. Optimal precision in the presence of uncertainty. Journal of Complexity, 1(2):170--196, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....along the0 real time axis. That is, they proved a lower bound on how close the real times can be when two processes adjusted clocks have the same value, whereas our result is a lower bound on how close the adjusted clock val ues can be at the same real time. 1talpern, Megiddo and Munshi [63] extended the resuits of [77] to other kinds of graphs besides just complete graphs, using the same basic kind of stretching arguments. The characterization for general graphs is not as nice as for complete graphs, however. 2.3 Shared Registers Now I reconsider shared memory asynchronous algo ....

J. Halpern, N. Megiddo, and A. Munshi. Optimal precision in the presence of uncertainty. Journal of Complexity, 1(2):170-196, December 1985.

....modeling decisions and a stimulus for the development of algorithm verification techniques. Similar results should be possible for real time systems. Some examples of complexity results that have already been obtained for real time systems are the many results on clock synchronization, including [8, 11, 17, 20, 32] (see [31] for a survey) In this paper, we embark on a study of complexity results for real time systems. We begin this study by considering timing based variations of certain problems that have previously been studied in asynchronous concurrent systems. In particular, we study a variant of the ....

HALI'ERN, J., MEGIDDO, N. AND MUNSHI, A. A. (1985), Optimal precision in the presence of uncertainty, J. Complexity 1, 170-196,

....time from the synchronization path and achieves precision in the order of 10s using commercial o# the shelf technology. Unknown system properties like non deterministic message delay and synchronization message pattern make it di#cult to apply bounds on the achievable precision as proposed by [8, 7, 10, 12, 11]. Therefore we propose an analysis of clock synchronization algorithms under completely unknown system specifications in terms of message delay and message pattern. Instead of bounds on the achievable precision, we propose two properties that describe good algorithms. Safe synchronization never ....

Joseph Y. Halpern, Nimrod Megiddo, and Ashfaq A. Munshi. Optimal precision in the presence of uncertainty. Journal of Complexity, 1(2):170--196, 1985.

....initial state q 0;i and a distinguished fail state. A configuration is a vector C = q 1 ; q n ) where q i is the local state of p i ; denote state i (C) q i . The initial configuration is the vector (q 0;1 ; q 0;n ) Processes communicate by sending messages 4 See [13, 22, 25, 27, 37, 39], for example. 5 These definitions could be expressed in terms of the general timed automaton model described in [1] and [29] however, we choose here to present the definitions directly, in order to avoid the intervening layer of definitions. 5 (taken from some alphabet M) to each other. A ....

Halpern, J. Y., Megiddo, N., and Munshi, A. A. Optimal precision in the presence of uncertainty. Journal of Complexity 1 (1985), 170--196.

....clock synchronization, which is beyond the scope of this thesis. 1. 2 Previous Work Different variants of the clock synchronization problem have been the target of a vast amount of research from both practical viewpoint (e.g. 26, 6, 24, 28, 1, 15] and theoretical viewpoint (e.g. [16, 19, 7, 13, 33, 3], surveys [31, 30] and references therein) the exact definition of the problem depends both on the intended use of the clocks and on the specific underlying system. The large number of variants is justified by the wide spectrum of applications. One of the popular variants studied theoretically ....

....In this thesis, numbers range over R [ f1; Gamma1g unless explicitly indicated otherwise. Square brackets are used to denote intervals, including the case of infinite intervals. 11 that gives optimal tightness in the worst possible scenario allowable by the system specifications. Halpern et al. [13] generalized the results of [19] to networks whose underlying topology is arbitrary, and whose message latency bounds may be different for each link. The main idea in the analysis of [13] is to formulate the problem as a linear program; solving this program, they find the worst case scenario, and ....

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J. Y. Halpern, N. Megiddo, and A. A. Munshi. Optimal precision in the presence of uncertainty. Journal of Complexity, 1:170--196, 1985.

....calculus of time bounds. Dolev et al. 8] use similar techniques to obtain synchronization algorithms for relativistic systems. Much effort has been devoted to studying internal synchronization, where the goal is to synchronize clocks within a system in which real time is not available (see, e.g. [11, 12, 6, 10, 24, 1], surveys [22, 21] and references therein) The approach of comparing the synchronization bounds to the best possible bound for the given execution was first presented by Attiya et al. in [1] where they studied internal synchronization. The work in [1] extended the work of Halpern et al. 10] ....

....24, 1] surveys [22, 21] and references therein) The approach of comparing the synchronization bounds to the best possible bound for the given execution was first presented by Attiya et al. in [1] where they studied internal synchronization. The work in [1] extended the work of Halpern et al. [10], which analyzed internal synchronization as a game against nature, which means that it is assumed that the execution should be taken as if it is generated by an adversary whose aim is to provide as little information as possible within the system specification. The work in [10] in turn, ....

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J. Y. Halpern, N. Megiddo, and A. A. Munshi. Optimal precision in the presence of uncertainty. Journal of Complexity, 1:170--196, 1985.

....Lundelius and Lynch [5] showed that the local clocks of n processors in a fully connected network with the same uncertainty u on each link cannot be synchronized any more closely than u Delta (1 Gamma 1 n ) They provide a simple algorithm that achieves this bound. Halpern et al. [3] subsequently extended this work to consider arbitrary topologies in which each directed edge may have a different uncertainty. They established a closed form expression for the optimal synchronization in a tree and a triangle. For the tree, the bound is equal to 1 2 diam, where diam is the ....

....with respect to the uncertainties on the links. For the general case, they show that the optimal synchronization is the solution of an optimization problem using linear programming techniques, but they do not give a closed form expression. In this paper we attempt to address open question 7 in [3]: it would be interesting to obtain precise formulas for the imprecision for a number of graphs that arise in practice. For an arbitrary undirected topology with arbitrary symmetric uncertainties, we prove a lower bound of 1 2 diam on the closeness of synchronization achievable, where diam ....

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J. Y. Halpern, N. Megiddo, and A. A. Munshi, "Optimal Precision in The Presence of Uncertainty," Journal of Complexity, vol. 1, pp. 170-196, 1985.

....bounds with a less precise dependency on the timing uncertainty than we obtain here. The work presented here is part of an emerging study of the real time behavior of distributed systems. Other work in this area includes the extensive literature on clock synchronization algorithms, for example, [10, 16, 20, 21, 30, 32], and on specific problems, such as mutual exclusion [3] synchronization [4, 29] leader election [6] and failure detection [18, 27] The rest of this paper is organized as follows. In Section 2, we present the definitions of the model and of the failure types we address. We next present two ....

Halpern, J. Y., Megiddo, N., and Munshi, A. A. Optimal precision in the presence of uncertainty. Journal of Complexity 1 (1985), 170--196.

....corrections both forward and backward that are called for by some clock synchronization protocol. In many cases it is desirable to provide a sequence of time values that is monotone nondecreasing and varies from the values corresponding to some standard or real time by at most a bounded rate [L, HMM]. However, for many clock synchronization protocols, it is more convenient to make corrections immediately and set clocks either forward or back by significant amounts. By using one logical clock directly in the synchronization protocol and reading time from another logical clock that amortizes ....

....first in order to smooth the changes and prevent time running backward, one can have the best of both worlds. This decoupling of clock synchronization from considerations of smoothness can simplify the consideration of smoothness of time given in many papers devoted to clock synchronization (v. [Cri, CS, L, HMM]) Finally, logical clocks can be used to simulate timed events at any desired rate. If software for a timed process is to be simulated and the software gets its time from a logical clock. Then another logical clock running at a different rate can be substituted almost immediately with no other ....

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J. Halpern, N. Megiddo, and A. Munshi, Optimal Precision in the Presence of Uncertainty, J. Complexity 1, 170-196, 1985.

....with far better properties than would be possible in asynchronous systems. One well studied problem in the context of systems with real time constraints is clock synchronization [Attiya, Herzberg, and Rajsbaum 1993; Dolev, Halpern, and Strong 1986; Halpern, Strong, Simons, and Dolev 1984; Halpern, Megiddo, and Munshi 1985; Lamport and Melliar Smith 1985; Lynch and Lundelius 1985; Patt Shamir and Rajsbaum 1994; Srikanth and Toueg 1987] see [Schneider 1987] and [Simons, Welch, and Lynch 1988] for surveys. This is an important problem because maintaining an good degree of synchronization between clocks is a central ....

....in order to perfectly synchronize their clocks. It is well known, however, that in many cases, no amount of interaction in which the processes share their information via communicated messages will enable the processes to perfectly synchronize their clocks (see [Dolev, Halpern, and Strong 1986; Halpern, Megiddo, and Munshi 1985; Lynch and Lundelius 1985] Thus, the fact that they have distributed knowledge about how to perfectly synchronize clocks can not be brought to bear on the problem. What is the source of the problem in this example Intuitively, the standard models of knowledge (and, in fact, many other models ....

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Halpern, J. Y., N. Megiddo, and A. Munshi (1985). Optimal precision in the presence of uncertainty. Journal of Complexity 1, 170--196.

....incur uncertain delays. A relatively simple case is when local clocks are accurate, i.e. run at the same speed, and there are upper and lower bounds for the delay on each link. Clock synchronization algorithms under this assumption, whose precision is optimal in the worst case, are described in [4, 11]. Subsequent work concentrated on clocks that may drift and on fault tolerance (e.g. 2, 7, 20, 21] see survey in [19] To achieve high precision, these algorithms require the existence of tight lower and upper bounds on message delay. However, in real systems it is often the uncertainty of ....

....several different delay assumptions. Such mixtures are quite common in practical, heterogeneous systems. For example, there are systems in which several local area (broadcast) networks are connected by bridges or (long distance) links. Our work extends the results of Halpern, Megiddo and Munshi [4]. Halpern et al. use linear programming techniques which do not illuminate the inherent difficulties of synchronizing clocks. We believe that our work gives a more precise understanding of the problem, explicitly showing what are the requirements of each step and thereby facilitating adaptation to ....

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J. Halpern, N. Megiddo and A. A. Munshi, "Optimal Precision in the Presence of Uncertainty, " J. Complexity, 1 (1985), pp. 170--196.

....are reliable, but both delays and clock drifts are uncertain (e.g. 7, 10] Although the algorithms are simple to state, their analyses tend to be complicated. Moreover, even for this case, no nontrivial lower bounds were known. The case of systems whose clocks are drift free is better understood [8, 6, 2]. In [8, 6] the worst possible behaviors of the system (within its specifications) are analyzed, and optimal protocols for the worst case are proposed. The protocols send one message per link, because in the worst case no additional information is gained by sending more messages. Recently, Attiya ....

....but both delays and clock drifts are uncertain (e.g. 7, 10] Although the algorithms are simple to state, their analyses tend to be complicated. Moreover, even for this case, no nontrivial lower bounds were known. The case of systems whose clocks are drift free is better understood [8, 6, 2] In [8, 6], the worst possible behaviors of the system (within its specifications) are analyzed, and optimal protocols for the worst case are proposed. The protocols send one message per link, because in the worst case no additional information is gained by sending more messages. Recently, Attiya et al. 2] ....

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J. Y. Halpern, N. Megiddo, and A. A. Munshi. Optimal precision in the presence of uncertainty. Journal of Complexity, 1:170--196, 1985.

....of broadcast messages and the ability to achieve certain goals in distributed systems. We have taken clock synchronization as a paradigm problem to study in this context because it has been so well studied, both in the presence of faults (see, for example, 1, 5, 9, 11, 13, 15] and without faults [8, 10, 12, 16]. The basic problem we consider is the same as that considered in [8, 12] we assume that each process has a clock that runs at the rate of real time, and the problem is to synchronize these clocks as tightly as possible. Of course, in practice, clocks drift apart. However, the drift is typically ....

.... We have taken clock synchronization as a paradigm problem to study in this context because it has been so well studied, both in the presence of faults (see, for example, 1, 5, 9, 11, 13, 15] and without faults [8, 10, 12, 16] The basic problem we consider is the same as that considered in [8, 12]: we assume that each process has a clock that runs at the rate of real time, and the problem is to synchronize these clocks as tightly as possible. Of course, in practice, clocks drift apart. However, the drift is typically small, and by ignoring it here, we can examine the impact of broadcasting ....

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J. Halpern, N. Megiddo and A. Munshi, "Optimal precision in the presence of uncertainty, " Journal of Complexity 1, 1985, pp. 170--196.

....signatures. The resynchronization algorithm is described in Section 3 and analyzed in Section 4. The worst case difference between logical clocks that is guaranteed by our algorithm is almost as small as possible, but a careful discussion of this property is beyond the scope of this paper (v. [DHS,HMM,LL]) We discuss issues related to initialization and joining in Section 5. In Section 6, we present a synchronous update service, which enables all correct processes to agree on which processes are currently joined; this service plays a key role in our join algorithm. The join algorithm is presented ....

....considers a model in which there exists a minimal bound on the time it takes a message to travel along a link. We have restricted our analysis to the simpler model based on A2. We leave it to the reader to verify that our results could also be obtained using the refined versions. As is shown in [HMM,LL], the tightness or precision of the synchronization need depend only on the uncertainty of message transmission and processing time, not on its upper bound. However, our experience suggests that for many practical environments, the uncertainty is essentially the upper bound, justifying this ....

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J.Y. Halpern, N. Megiddo, and A. Munshi, "Optimal precision in the presence of uncertainty," Journal of Complexity 1, 1985, pp. 170-196.

....about the precise instant at which each processor starts functioning, and about exactly how much time each message takes to be delivered. In Appendix B we give a precise formulation of the notion of temporal imprecision, which captures these properties, and use methods derived from [DHS86] and [HMM85] to prove the following result: Theorem 8 : Let R be a system with temporal imprecision, let I be a knowledge interpretation for R, and let jGj 2. Then for all runs r 2 R, times t, and formulas it is the case that (I; r; t) j= CG iff (I; r; 0) j= CG . Since practical systems turn out to ....

.... to suppose that if the system designer considers it possible that a message will take time T to be delivered, then for some sufficiently small ffi 0, he will also consider it possible that the delivery time is anywhere in the interval (T Gamma ffi; T ffi) in this we differ slightly from [DHS86, HMM85]. We define f l to be a message delivery function for link l if f l : N (L l ; H l ) A run r is consistent with f l if for all n 2 N, f l (n) is the delivery time of the n th message in r on link l. A system R has bounded but uncertain message delivery times if for all links l there exist ....

J. Y. Halpern, N. Megiddo, and A. Munshi. Optimal precision in the presence of uncertainty. Journal of Complexity, 1:170--196, 1985.

.... = r j (m 1) Intuitively, in a system with temporal imprecision, i is uncertain about j s clock reading; at the point (r; m) process i cannot tell whether j s clock is characterized by j s local state at (r; m) or j s local state at (r; m 1) Techniques from the distributed systems literature [DHS86, HMM85] can be used to show that any system in which, roughly speaking, there is some initial uncertainty regarding relative clock readings and uncertainty regarding exact message transmission times must have temporal imprecision. Systems with temporal imprecision turn out to have the property that no ....

J. Y. Halpern, N. Megiddo, and A. Munshi. Optimal precision in the presence of uncertainty. Journal of Complexity, 1:170--196, 1985.

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Joseph Y. Halpern, Nimrod Megiddo, and Ashfaq A. Munshi. Optimal precision in the presence of uncertainty. Journal of Complexity, 1(2):170--196, 1985.

No context found.

J. Y. Halpern, N. Megiddo, and A. A. Munshi. Optimal precision in the presence of uncertainty. Journal of Complexity, 1(2):170--196, Dec. 1985.

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Joseph Y. Halpern, Nimrod Megiddo, and Ashfaq A. Munshi. Optimal precision in the presence of uncertainty. Journal of Complexity, 1(2), pages 170--196, December 1985.

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J. Halpern, N. Megiddo, A. Munshi, Optimal Precision in the Presence of Uncertainty, J. Complexity 1, 1985, 170-196.

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