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.
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
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.
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...
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.
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»
14707750
Probability Update: Conditioning vs. Cross-Entropy
Conditioning is the generally agreed-upon method for updating probability distributions when one learns that an event is certainly true. But it has been argued that we need other rules, in particular the rule of cross-entropy minimization, to handle updates that involve uncertain information. In this paper we re-examine such a case: van Fraassen's Judy Benjamin problem [1987], which in essence asks how one might update given the value of a conditional probability. We argue that--contrary to the suggestions in the literature--it is possible to use simple conditionalization in this case, and thereby obtain answers that agree fully with intuition. This contrasts with proposals such as cross-entropy, which are easier to apply but can give unsatisfactory answers. Based on the lessons from this example, we speculate on some general philosophical issues concerning probability update.
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.
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.
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.
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.