2990183
Performing work efficiently in the presence of faults
We consider a system of t synchronous processes that communicate only by sending messages to one another, and together the processes must perform n independent units of work. Processes may fail by crashing; we want to guarantee that in every execution of the protocol in which at least one process survives, all n units of work will be performed. We consider three parameters: the number of messages sent, the total number of units of work performed (including multiplicities), and time. We present three protocols for solving the problem. All three are work optimal, doing O(n+t) work. The rst has moderate costs in the remaining two parameters, sends O(t p t) messages, and takes O(n+t) time. This protocol can be easily modied to run in any completely asynchronous system equipped with a failure detection mechanism. The second sends only O(tlogt) messages, but its running time is large (O(t 2 (n+t)2 n+t )). The third is essentially time optimal in the (usual) case in which there are no failures, and its time complexity degrades gracefully as the number of failures increases.
1225089
Defining Explanation in Probabilistic Systems
As probabilistic systems gain popularity and are coming into wider use, the need for a mechanism that explains the system's findings and recommendations becomes more critical. The system will also need a mechanism for ordering competing explanations. We examine two representative approaches to explanation in the literature-- one due to Gardenfors and one due to Pearl--and show that both suffer from significant problems. We propose an approach to defining a notion of "better explanation" that combines some of the features of both together with more recent work by Pearl and others on causality.
8145017
Characterizing the Common Prior Assumption
Abstract Logical characterizations of the common prior assumption (CPA) are investigated. Two approaches are considered. The first is called frame distinguishability , and is similar in spirit to the approaches considered in the economics literature. Results similar to those obtained in the economics literature are proved here as well, namely, that we can distinguish finite spaces that satisfy the CPA from those that do not in terms of disagreements in expectation. However, it is shown that, for the language used here, no formulas can distinguish infinite spaces satisfying the CPA from those that do not. The second approach considered is that of finding a sound and complete axiomatization. Such an axiomatization is provided; again, the key axiom involves disagreements in expectation. The same axiom system is shown to be sound and complete both in the finite and the infinite case. Thus, the two approaches to characterizing the CPA behave quite differently in the case of infinite spaces. Journal of Economic Literature Classification Numbers: C70, D80.
3055934
A knowledge-theoretic analysis of uniform distributed coordination and failure detectors
Abstract.It is shown that, in a precise sense, if there is no bound on the number of faulty processes in a system with unreliable but fair communication, Uniform Distributed Coordination (UDC) can be attained if and only if a system has perfect failure detectors. This result is generalized to the case where there is a bound t on the number of faulty processes. It is shown that a certain type of generalized failure detector is necessary and sufficient for achieving UDC in a context with at most t faulty processes. Reasoning about processes’ knowledge as to which other processes are faulty plays a key role in the analysis.
23622807
Time to publication: a progress report
The process of submitting a paper to a journal can be incredibly frustrating for authors. Practically everyone who has been active in research for more than a few years has either first-or secondhand experience with some real horror stories. One of my goals when I took over JACM was to ease some of these frustrations, by speeding up the time to publication. I'd like to give you a sense of our progress in reaching that goal. Traditionally, a paper submitted to JACM went through many steps: the paper was submitted to the editor-in-chief; the editor-in-chief sent it to an editor; the editor sent it to referees; the paper went through one or more iterations between the referees, editor, editor-in-chief, and author(s); if the paper was accepted, it went on to the publication queue; authors received galleys and corrected them; and the paper finally appeared. As a result, the median time from submission to final acceptance for papers published in 1997 was 20 months. I would like to cut this down to 12 months. Often the most frustrating experience for authors is to submit a paper and then, after more than a year of waiting, to discover that it has been rejected. I don't have reliable statistics yet for how long such papers were in the system, but I would like to see significant progress here too. I would expect that the median time in the system for papers that are ultimately rejected will be 4 months. My predecessor, Tom Leighton, focused on what was the major cause of delay—the amount of time an accepted paper waited in the publication queue before it appeared. This wait used to be measured in years. The fact that the mean time to publication for 1997 was 20 months already shows how significant the improvement has been here. Currently (April 1998) the JACM web site shows that there are 19 papers in the queue, which means that the wait is approximately 3 issues, or 6 months. Since it is considered dangerous for an editor-in-chief to have too small a backlog, this is about the best that can be expected as far as the publication queue, at least until JACM goes completely electronic. Note, however, that final papers submitted in postscript are posted on the web site within a few days of submission; the papers on the queue are available to the world almost immediately. What …
10886930
Belief Revision with Unreliable Observations
Research in belief revision has been dominated by work that lies firmly within the classic AGM paradigm, characterized by a well-known set of postulates governing the behavior of "rational" revision functions. A postulate that is rarely criticized is the success postulate: the result of revising by an observed proposition ? results in belief in ?. This postulate, however, is often undesirable in settings where an agent's observations may be imprecise or noisy. We propose a semantics that captures a new ontology for studying revision functions, which can handle noisy observations in a natural way while retaining the classical AGM model as a special case. We present a characterization theorem for our semantics, and describe a number of natural special cases that allow ease of specification and reasoning with revision functions. In particular, by making the Markov assumption, we can easily specify and reason about revision.
2908780
Irrelevance and Conditioning in First-Order Probabilistic Logic
First-order probabilistic logic is a powerful knowledge representation language. Unfortunately, deductive reasoning based on the standard semantics for this logic does not support certain desirable patterns of reasoning, such as indifference to irrelevant information or substitution of constants into universal rules. We show that both these patterns rely on a first-order version of probabilistic independence, and provide semantic conditions to capture them. The resulting insight enables us to understand the effect of conditioning on independence, and allows us to describe a procedure for determining when independencies are preserved under conditioning. We apply this procedure in the context of a sound and powerful inference algorithm for reasoning from statistical knowledge bases.
16302257
Message-optimal protocols for Byzantine Agreement
It is often important for the correct processes in a distributed system to reach agreement, despite the presence of some faulty processes. Byzantine Agreement (BA) is a paradigm problem that attempts to isolate the key features of reaching agreement. We focus here on the number of messages required to reach BA, with particular emphasis on the number of messages required in thefailure-free runs, since these are the ones that occur most often in practice. The number of messages required is sensitive to the types of failures considered. In earlier work, Amduret al. (1992) established tight upper and lower bounds on the worst- and average-case number of messages required in failure-free runs for crash failures. We provide tight upper and lower bounds for all remaining types of failures that have been considered in the literature on the BA problem: receiving omission, sending omission, and general omission failures, as well as arbitrary failures with or without message authentication. We also establish a tradeoff between number of rounds and number of messages in the failure-free runs required to reach agreement in the case of crash, sending, and general omission failures.
6199093
Fault-tolerant clock synchronization
This paper gives two simple efficient distributed algorithms: one for keeping clocks in a network synchronized and one for allowing new processors to join the network with their clocks synchronized. The algorithms tolerate both link and node failures of any type. The algorithm for maintaining synchronization will work for arbitrary networks (rather than just completely connected networks) and tolerates any number of processor or communication link faults as long as the correct processors remain connected by fault-free paths. It thus represents an improvement over other clock synchronization algorithms such as [LM1,LM2,LL1]. Our algorithm for allowing new processors to join requires that more than half the processors be correct, a requirement which is provably necessary.
5516016
Naming and Identity in a Multi-Agent Epistemic Logic
7319496
Statistical Foundations for Default Reasoning
We describe a new approach to default, reasoning, based on a principle on indifference among possible worlds. We interpret default rules as extreme statistical statements, thus obtaining a knowledge base KB comprised of statistical and first-order statements. We then assign equal probability to all worlds consistent with KB in order to assign a degree of belief to a statement Φ. The degree of belief can be used to decide whether to defeasibly conclude Φ. Various natural patterns of reasoning, such as a preference for more specific defaults, indifference to irrelevant information, and the ability to combine independent pieces of evidence, turn out to follow naturally from this technique. Furthermore, our approach is not restricted to default reasoning; it supports a spectrum of reasoning, from quantitative to qualitative. It is also related to other systems for default reasoning. In particular, we show that the work of [Goldszmidt et al., 1990], which applies maximum entropy ideas to --semantics, can be embedded in our framework.