3,412 research outputs found
A probabilistic analysis of a leader election algorithm
A {\em leader election} algorithm is an elimination process that divides
recursively into tow subgroups an initial group of n items, eliminates one
subgroup and continues the procedure until a subgroup is of size 1. In this
paper the biased case is analyzed. We are interested in the {\em cost} of the
algorithm, i.e. the number of operations needed until the algorithm stops.
Using a probabilistic approach, the asymptotic behavior of the algorithm is
shown to be related to the behavior of a hitting time of two random sequences
on [0,1]
Automated Synthesis of Distributed Self-Stabilizing Protocols
In this paper, we introduce an SMT-based method that automatically
synthesizes a distributed self-stabilizing protocol from a given high-level
specification and network topology. Unlike existing approaches, where synthesis
algorithms require the explicit description of the set of legitimate states,
our technique only needs the temporal behavior of the protocol. We extend our
approach to synthesize ideal-stabilizing protocols, where every state is
legitimate. We also extend our technique to synthesize monotonic-stabilizing
protocols, where during recovery, each process can execute an most once one
action. Our proposed methods are fully implemented and we report successful
synthesis of well-known protocols such as Dijkstra's token ring, a
self-stabilizing version of Raymond's mutual exclusion algorithm,
ideal-stabilizing leader election and local mutual exclusion, as well as
monotonic-stabilizing maximal independent set and distributed Grundy coloring
Shift-Symmetric Configurations in Two-Dimensional Cellular Automata: Irreversibility, Insolvability, and Enumeration
The search for symmetry as an unusual yet profoundly appealing phenomenon,
and the origin of regular, repeating configuration patterns have long been a
central focus of complexity science and physics. To better grasp and understand
symmetry of configurations in decentralized toroidal architectures, we employ
group-theoretic methods, which allow us to identify and enumerate these inputs,
and argue about irreversible system behaviors with undesired effects on many
computational problems. The concept of so-called configuration shift-symmetry
is applied to two-dimensional cellular automata as an ideal model of
computation. Regardless of the transition function, the results show the
universal insolvability of crucial distributed tasks, such as leader election,
pattern recognition, hashing, and encryption. By using compact enumeration
formulas and bounding the number of shift-symmetric configurations for a given
lattice size, we efficiently calculate the probability of a configuration being
shift-symmetric for a uniform or density-uniform distribution. Further, we
devise an algorithm detecting the presence of shift-symmetry in a
configuration.
Given the resource constraints, the enumeration and probability formulas can
directly help to lower the minimal expected error and provide recommendations
for system's size and initialization. Besides cellular automata, the
shift-symmetry analysis can be used to study the non-linear behavior in various
synchronous rule-based systems that include inference engines, Boolean
networks, neural networks, and systolic arrays.Comment: 22 pages, 9 figures, 2 appendice
Leader Election for Anonymous Asynchronous Agents in Arbitrary Networks
We study the problem of leader election among mobile agents operating in an
arbitrary network modeled as an undirected graph. Nodes of the network are
unlabeled and all agents are identical. Hence the only way to elect a leader
among agents is by exploiting asymmetries in their initial positions in the
graph. Agents do not know the graph or their positions in it, hence they must
gain this knowledge by navigating in the graph and share it with other agents
to accomplish leader election. This can be done using meetings of agents, which
is difficult because of their asynchronous nature: an adversary has total
control over the speed of agents. When can a leader be elected in this
adversarial scenario and how to do it? We give a complete answer to this
question by characterizing all initial configurations for which leader election
is possible and by constructing an algorithm that accomplishes leader election
for all configurations for which this can be done
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