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19
Randomized Algorithms
, 1995
"... Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. Growth has been fueled by the two major benefits of randomization: simplicity and speed. For many applications a randomized algorithm is the fastest algorithm available, or the simp ..."
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Cited by 1876 (38 self)
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Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. Growth has been fueled by the two major benefits of randomization: simplicity and speed. For many applications a randomized algorithm is the fastest algorithm available, or the simplest, or both. A randomized algorithm is an algorithm that uses random numbers to influence the choices it makes in the course of its computation. Thus its behavior (typically quantified as running time or quality of output) varies from
Symmetry Breaking In Distributed Networks
 Information and Computation
, 1981
"... Given a ring of n processors it is required to design the processors such that they will be able to choose a leader (a uniquely designated processor) by sending messages along the ring. If the processors are indistinguishable then there exists no deterministic algorithm to solve the problem. To over ..."
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Cited by 70 (0 self)
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Given a ring of n processors it is required to design the processors such that they will be able to choose a leader (a uniquely designated processor) by sending messages along the ring. If the processors are indistinguishable then there exists no deterministic algorithm to solve the problem. To overcome this difficulty, probabilistic algorithms are proposed. The algorithms may run forever but they terminate within finite time on the average. For the synchronous case several algorithms are presented: The simplest requires, on the average, the transmission of no more than 2.442n bits and O (n) time. More sophisticated algorithms trade time for communication complexity. If the processors work asynchronously then on the average O (nlogn) bits are transmitted. In the above cases the size of the ring was assumed to be known to all the processors. If the size is not known then finding it may be done only with high probability: any algorithm may yield incorrect results (with nonzero probabilit...
The Mutual Exclusion Problem  Part II: Statement and Solutions
, 2000
"... The theory developed in Part I is used to state the mutual exclusion problem and several additional fairness and failuretolerance requirements. Four "distributed " Nprocess solutions are given, ranging from a solution requiring only one communication bit per process that permits individual starvat ..."
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Cited by 54 (2 self)
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The theory developed in Part I is used to state the mutual exclusion problem and several additional fairness and failuretolerance requirements. Four "distributed " Nprocess solutions are given, ranging from a solution requiring only one communication bit per process that permits individual starvation, to one requiring about N ! communication bits per process that satisfies every reasonable fairness and failuretolerance requirement that we can conceive of. Contents 1 Introduction 3 2 The Problem 4 2.1 Basic Requirements . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Fairness Requirements . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Premature Termination . . . . . . . . . . . . . . . . . . . . . 8 2.4 Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3 The Solutions 14 3.1 The Mutual Exclusion Protocol . . . . . . . . . . . . . . . . . 15 3.2 The OneBit Solution . . . . . . . . . . . . . . . . . . . . . . 17 3.3 A Digression . . . . . . . . . . . ...
Hundreds of Impossibility Results for Distributed Computing
 Distributed Computing
, 2003
"... We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include synchrony, faulttolerance, different communication media, and randomization. The resource bounds refe ..."
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Cited by 40 (4 self)
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We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include synchrony, faulttolerance, different communication media, and randomization. The resource bounds refer to time, space and message complexity. These results are useful in understanding the inherent difficulty of individual problems and in studying the power of different models of distributed computing.
Distributing Identity
, 1999
"... This paper considers distributed protocols for assigning IDs. ..."
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Cited by 29 (0 self)
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This paper considers distributed protocols for assigning IDs.
Electric Field Imaging
, 1999
"... The physical user interface is an increasingly significant factor limiting the effectiveness of our interactions with and through technology. This thesis introduces Electric Field Imaging, a new physical channel and inference framework for machine perception of human action. Though electric field se ..."
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Cited by 18 (5 self)
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The physical user interface is an increasingly significant factor limiting the effectiveness of our interactions with and through technology. This thesis introduces Electric Field Imaging, a new physical channel and inference framework for machine perception of human action. Though electric field sensing is an important sensory modality for several species of fish, it has not been seriously explored as a channel for machine perception. Technological applications of field sensing, from the Theremin to the capacitive elevator button, have been limited to simple proximity detection tasks. This thesis presents a solution to the inverse problem of inferring geometrical information about the configuration and motion of the human body from electric field measurements. It also presents simple, inexpensive hardware and signal processing techniques for making the field measurements, and several new applications of electric field sensing. The signal
Taskstructured probabilistic I/O automata
, 2006
"... Modeling frameworks such as Probabilistic I/O Automata (PIOA) and Markov Decision Processes permit both probabilistic and nondeterministic choices. In order to use such frameworks to express claims about probabilities of events, one needs mechanisms for resolving nondeterministic choices. For PIOAs, ..."
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Cited by 18 (12 self)
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Modeling frameworks such as Probabilistic I/O Automata (PIOA) and Markov Decision Processes permit both probabilistic and nondeterministic choices. In order to use such frameworks to express claims about probabilities of events, one needs mechanisms for resolving nondeterministic choices. For PIOAs, nondeterministic choices have traditionally been resolved by schedulers that have perfect information about the past execution. However, such schedulers are too powerful for certain settings, such as cryptographic protocol analysis, where information must sometimes be hidden. Here, we propose a new, less powerful nondeterminismresolution mechanism for PIOAs, consisting of tasks and local schedulers. Tasks are equivalence classes of system actions that are scheduled by oblivious, global task sequences. Local schedulers resolve nondeterminism within system components, based on local information only. The resulting taskPIOA framework yields simple notions of external behavior and implementation, and supports simple compositionality results. We also define a new kind of simulation relation, and show it to be sound for proving implementation. We illustrate the potential of the taskPIOA framework by outlining its use in verifying an Oblivious Transfer protocol.
Naming Symmetric Processes Using Shared Variables
 Distributed Computing
, 1994
"... Implementations of interprocess communication and synchronization in distributed systems usually rely on the existence of unique ids for the processes. We consider the problem of generating such ids for identical processes in a sharedvariable system. A randomized protocol that assigns distinct ids ..."
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Cited by 11 (0 self)
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Implementations of interprocess communication and synchronization in distributed systems usually rely on the existence of unique ids for the processes. We consider the problem of generating such ids for identical processes in a sharedvariable system. A randomized protocol that assigns distinct ids to the processes within an expected polynomial number of rounds using a polynomial number of boolean atomic variables is presented.
Verification by probabilistic abstraction
 Weizmann Institute of Science Technical Report
, 2003
"... Abstract. The paper studies automatic verification of liveness properties with probability 1 over parameterized programs that include probabilistic transitions, and proposes two novel approaches to the problem. The first approach is based on a Planner that occasionally determines the outcome of a fi ..."
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Cited by 5 (2 self)
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Abstract. The paper studies automatic verification of liveness properties with probability 1 over parameterized programs that include probabilistic transitions, and proposes two novel approaches to the problem. The first approach is based on a Planner that occasionally determines the outcome of a finite sequence of “random” choices, while the other random choices are performed nondeterministically. Using a Planner, a probabilistic protocol can be treated just like a nonprobabilistic one and verified as such. The second approach is based on γfairness, a notion of fairness that is sound and complete for verifying simple temporal properties (whose only temporal operators are and) over finitestate systems. The paper presents a symbolic model checker based on γfairness. We then show how the network invariant approach can be adapted to accommodate probabilistic protocols. The utility of the Planner approach is demonstrated on a probabilistic mutual exclusion protocol. The utility of the approach of γfairness with network invariants is demonstrated on Lehman and Rabin’s Courteous Philosophers algorithm. 1
Solvability In Asynchronous Environments II: Finite Interactive Tasks
 SIAM Journal on Computing
, 2000
"... Identifying what problems can be solved in a given distributed system is a central question in distributed computing. In this series of works, we study this question in the context of asynchronous fault tolerant systems that can execute consensus. These systems can be those executing deterministic p ..."
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Cited by 3 (0 self)
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Identifying what problems can be solved in a given distributed system is a central question in distributed computing. In this series of works, we study this question in the context of asynchronous fault tolerant systems that can execute consensus. These systems can be those executing deterministic protocols with access to a consensus routine or those running randomized errorfree protocols. A previous work handled the class of distributed decision tasks. In these tasks, each processor receives one local input and has to respond with one local output.