8423368
A characterization of eventual Byzantine agreement
We investigate eventual Byzantine agreement (EBA) in the crash and omission failure models. The emphasis is on characterizing optimal EBA protocols in terms of the states of knowledge required by the processors in order to attain EBA. It is well known that common knowledge among the nonfaulty processors is a necessary and sufficient condition for attaining simultaneous Byzantine agreement (SBA). We define a new variant of common knowledge, which we call continual common knowledge, in terms of which we can characterize necessary and sufficient conditions for attaining EBA. Using our characterization, we provide a technique that allows us to start with any EBA protocol, apply a certain construction twice, and arrive at an optimal EBA protocol.
152014
Causality, Responsibility, and Blame: A Structural-Model Approach
This talk provides an overview of work that I have done with Hana Chockler, Orna Kupferman, and Judea Pearl (H. Chockler and J. Y. Halpern, 2004), (H. Chockler, et al., 2003), (J. Y. Halpern and J. Pearl, 2005), on defining notions such as causality, explanation, responsibility, and blame. I first review the Halpern-Pearl definition of causality, what it means that A is a cause of B, and show how it handles well some standard problems of causality. This definition of causality (like most in the literature) views causality as an all-or-nothing concept. Either A is a cause of B or it is not. I show how it can be extended to take into account the degree of responsibility of A for B. For example, if someone wins an election 11-0, each person is less responsible for his victory than if he had won 6-5. Finally, I show how this notion of degree of responsibility can be used to provide insight into model checking notions such as coverage
15233558
A new look at fault tolerant network routing
Consider a communication network G in which a limited number of link and/or node faults F might occur. A routing &rgr; for the network (a fixed path between each pair of nodes) must be chosen without any knowledge of which components might become faulty. Choosing a good routing corresponds to bounding the diameter of the surviving route graph R(G,&rgr;)/F, where two nonfaulty nodes are joined by an edge if there are no faults on the route between them. We prove a number of results concerning the diameter of surviving route graphs. We show that if &rgr; is a minimal length routing, then the diameter of R(G,&rgr;)/F can be on the order of the number of nodes of G, even if F consists of only a single node. However, if G is the n-dimensional cube, the diameter of R(G,&rgr;)/F≤3 for any minimal length routing &rgr; and any set of faults F with |F|<n. We also show that if F consists only of edges and does not disconnect G, then the diameter of R(G,&rgr;)/F is ≤ 3|F|+1, while if F consists only of nodes and does not disconnect G, then the diameter of R(G,&rgr;)/F is ≤ the sum of the degrees of the nodes in F, where in both cases &rgr; is an arbitrary minimal length routing. We conclude with one of the most important contributions of this paper: a list of interesting and apparently difficult open problems.
47316226
Equations Between Regular Terms and an Application to Process Logic
Regular terms with the Kleene operations $ \cup $, ; and $ * $ can be thought of as operators on languages, generating other languages. An equation $\tau _1 = \tau _2 $ between two such terms is said to be satisfiable just in case languages exist which make this equation true. We show that the satisfiability problem even for $ * $-free regular terms is undecidable. Similar techniques are used to show that a very natural extension of the Process Logic of Harel, Kozen and Parikh is undecidable.
14995360
A model-theoretic analysis of knowledge
A general semantic model of knowledge is introduced, to allow reasoning about statements such as «He knows that I know whether or not she knows whether or not it is raining». This approach more naturally models a state of knowledge than previous proposals (including Kripke structures). Using this notion of model, a model theory for knowledge is developed. This theory enables one to interpret the notion of a «finite amount of information»
215949262
Knowledge, probability, and adversaries
What should it mean for an agent to know or believe an assertion is true with probability 9.99? Different papers [2, 6, 15] give different answers, choosing to use quite different probability space...
23268703
A knowledge-theoretic analysis of uniform distributed coordination and failure detectors
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.
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.
227589
Updating Sets of Probabilities
There are several well-known justifications for conditioning as the appropriate method for updating a single probability measure, given an observation. However, there is a significant body of work arguing for sets of probability measures, rather than single measures, as a more realistic model of uncertainty. Conditioning still makes sense in this context--we can simply condition each measure in the set individually, then combine the results--and, indeed, it seems to be the prel ferred updating procedure in the literature. But how justified is conditioning in this richer setting? Here we show, by considering an axiomatic account of conditioning given by van Fraassen, that the single-measure and sets-of-measures cases are very different. We show that van Fraassen's axiomatization for the former case is nowhere near sufficient for updating sets of measures. We give a considerably longer (and not as compelling) list of axioms that together force conditioning in this setting, and describe other update methods that are allowed once any of these axioms is dropped.
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.
10093090
A decision-theoretic approach to reliable message delivery
Summary. We argue that the tools of decision theory should be taken more seriously in the specification and analysis of systems. We illustrate this by considering a simple problem involving reliable communication, showing how considerations of utility and probability can be used to decide when it is worth sending heartbeat messages and, if they are sent, how often they should be sent.