G. Neiger and S. Toueg. Simulating real-time clocks and common knowledge in distributed systems. Journal of the ACM, 40(2):334--367, 1993.  Home/Search   Document Not in Database   Summary   ACM   TOC   Related Articles   Check

.... is true. Knowledge based programs are an attempt to capture the intuition that what an agent does depends on what it knows. They have already met with do forever if K(x = 0) then y : y 1 end end; Figure 2: The program Pg 2 1 some degree of success, having been used in papers such as [3, 8, 11, 12, 19, 17, 21, 22] both to help in the design of new protocols and to clarify the understanding of existing protocols. However, Sanders [25] has pointed out what seems to be a counterintuitive property of knowledge based programs. Roughly speaking, she claims that knowledge based programs do not satisfy a certain ....

G. Neiger and S. Toueg. Simulating real-time clocks and common knowledge in distributed systems. Journal of the ACM, 40(2):334--367, 1993.

....Their goal was to provide a formal semantics for programs with tests for knowledge such as if K(x = 0) do y : y 1, where K(x = 0) should be read as you know that x = 0 . Unfortunately, the technical definition of knowledgebased protocols given in [HF85] later simplified somewhat in [HF89, Maz91, NT93]) had a number of deficiencies, which made it somewhat difficult to use as a tool for program design. For one thing, knowledge based protocols were defined as functions from local states and systems to actions. Thus, the definition did not directly capture the intuition that knowledge based ....

G. Neiger and S. Toueg. Simulating real-time clocks and common knowledge in distributed systems. Journal of the ACM, 40(2):334-- 367, 1993.

....human agents or robots. Of course, we also want the model to be natural and intuitive, and lend itself easily to most types of formal analysis. We describe a model here that we believe fulfills these properties. The model is motivated by previous work on knowledge based analyses of protocols [CM86, DM90, FHV92, FI86, Had87, HF85, HM90, HZ92, MT88, NT93, PR85] (see [Hal87] for an overview) In all of these papers (and many others that have appeared in the literature) a protocol is identified with a set of runs or executions. We intuitively think of a run as a complete description of all the relevant events that occur in a system over time, where for ....

....view it as a function from a pair consisting of a local state and an interpreted system to actions. We essentially took the former approach in [HF85] where the notion of knowledge based protocol was introduced; the approach we take here to the definition of knowledge based protocols was taken in [NT93]. Formally, fix a set G L e Theta L 1 Theta Delta Delta Delta Theta L n of global states and a set A i of actions for process i, and let INT (G) be the set of all interpreted systems I = R; such that for every run r 2 R, all the global states in r are in G. Then a knowledge based ....

G. Neiger and S. Toueg. Simulating real-time clocks and common knowledge in distributed systems. Journal of the ACM, 40(2):334--367, 1993.

....it knows. They have already met with some degree of success, having been used in papers such as [Dwork and Moses 1990; Hadzilacos 1987; Halpern, Moses, and Waarts 1990; Halpern and Zuck 1992; Mazer and Lochovsky 1990; Mazer 1990; Moses and Kislev 1993; Moses and Tuttle 1988; Neiger and Bazzi 1992; Neiger and Toueg 1993] both to help in the design of new protocols and to clarify the understanding of existing protocols. However, as we show here, there are cases when, used naively, knowedge based programs may exhibit counterintuitive behavior. We then show how this can be overcome by the use of counterfactuals ....

Neiger, G. and S. Toueg (1993). Simulating real-time clocks and common knowledge in distributed systems. Journal of the ACM 40(2), 334--367.

....by the processors. The processors are state machines that possibly have clocks, where a clock is a monotone nondecreasing function of real time. If a processor has a clock, then we assume that its clock reading is part of its state. This is in contrast to the approach taken by Neiger and Toueg in [NT93]; the difference is purely a matter of taste. The processors communicate with each other by sending messages along the links in the network. A run r of a distributed system is a description of an execution of the system, from time 0 until the end of the execution. We assume for simplicity that ....

....can be thought of as actually attaining timestamped common knowledge of the decision value, with the timestamp being the end of phase k . Indeed, protocols like the atomic broadcast protocol of [CASD85] are designed exactly for the purpose of attaining timestamped common knowledge. See [NT93] for more discussion of timestamped common knowledge. 13 Internal knowledge consistency We have seen that common knowledge closely corresponds to the ability to perform simultaneous actions. In the last few sections we introduced a number of related states of knowledge corresponding to weaker ....

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G. Neiger and S. Toueg. Simulating real-time clocks and common knowledge in distributed systems. Journal of the ACM, 40(2):334--367, 1993.

....an agent knows if, in all situations consistent with the agent s information, is true. Knowledge based programs are an attempt to capture the intuition that what an agent does depends on what it knows. They have already met with some degree of success, having been used in papers such as [DM90, Had87, HMW90, HZ92, ML90, Maz90, MT88, NT93] both to help in the design of new protocols and to clarify the understanding of existing protocols. However, Sanders [San91] has pointed out what seems to be a counterintuitive property of knowledge based programs. Roughly speaking, she claims that knowledge based programs do not satisfy a ....

G. Neiger and S. Toueg. Simulating real-time clocks and common knowledge in distributed systems. Journal of the ACM, 40(2):334--367, 1993.

....in fact by different groups of people. It has been suggested [HM90] that a useful way to analyze distributed systems is in terms of knowledge and how communication changes the processes state of knowledge. The role of knowledge in distributed systems has by now been extensively studied [CM86, DM90, FHV92, FI86, Had87, Hal87, HF85, HV86, LR86, MT88, NT93, PR85] (see [Hal87] for an overview) In this paper, we use reasoning about knowledge to help design and verify a family of protocols that deal with a standard problem of data communication that we call the sequence transmission problem. The problem is easily stated: Consider two processes, called the ....

....do not have a general methodology for deriving a knowledge based protocol, nor a general methodology for implementing it as a standard protocol once we have found it. Nevertheless, we feel that the knowledge based approach will be an aid in designing and verifying protocols. Recent papers, such as [Had87, HMT88, HMW90, ML90, Maz90, NT93], that have used the knowledge based approach lend credence to our feelings. Acknowledgements: We would particularly like to thank Brent Hailpern, who started us thinking about the AUY protocols. We also thank Ron Fagin, Mike Fischer, Brent Hailpern, Yoni Malachi, Murray Mazer, Yoram Moses, and ....

G. Neiger and S. Toueg. Simulating real-time clocks and common knowledge in distributed systems. Journal of the ACM, 40(2):334--367, 1993.

....that the children answer simultaneously, then the coarse model would not have been adequate. For a more formal presentation of our approach, see [FHMV95] The observation that whether or not common knowledge is attainable depends in part on how we model time was made in a number of earlier papers [FI86, HM90, Kur86, Nei88, NT93]. Our approach formalizes this observation and offers a rigorous way to determine when the coarse model is adequate. 7 Approximations of Common Knowledge Section 4 shows that common knowledge captures the state of knowledge resulting from simultaneous events. It also shows, however, that in the ....

G. Neiger and S. Toueg. Simulating real-time clocks and common knowledge in distributed systems. Journal of the ACM, 40(2):334--367, 1993.

....Their goal was to provide a formal semantics for programs with tests for knowledge such as if K(x = 0) do y : y 1, where K(x = 0) should be read as you know that x = 0 . Unfortunately, the technical definition of knowledge based protocols given in [HF85] later simplified somewhat in [HF89, Maz91, NT93]) had a number of deficiencies, which made it somewhat difficult to use as a tool for program design. For one thing, a knowledge based protocol was defined as a function from local states and systems to actions (we provide details in Section 3.2) Thus, the definition did not directly capture the ....

G. Neiger and S. Toueg. Simulating real-time clocks and common knowledge in distributed systems. Journal of the ACM, 40(2):334--367, 1993.

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