33,310 research outputs found
The probability of nontrivial common knowledge
We study the probability that two or more agents can attain common knowledge of nontrivial events when the size of the state space grows large. We adopt the standard epistemic model where the knowledge of an agent is represented by a partition of the state space. Each agent is endowed with a partition generated by a random scheme. Assuming that agents' partitions are independently and identically distributed, we prove that the asymptotic probability of nontrivial common knowledge undergoes a phase transition. Regardless of the number of agents, when their cognitive capacity is sufficiently large, the probability goes to one; and when it is small, it goes to zero.Common knowledge; Epistemic game theory; Random partitions
The probability of nontrivial common knowledge
We study the probability that two or more agents can attain common knowledge of nontrivial events when the size of the state space grows large. We adopt the standard epistemic model where the knowledge of an agent is represented by a partition of the state space. Each agent is endowed with a partition generated by a random scheme consistent with his cognitive capacity. Assuming that agents' partitions are independently distributed, we prove that the asymptotic probability of nontrivial common knowledge undergoes a phase transition. Regardless of the number of agents, when their cognitive capacity is sufficiently large, the probability goes to one; and when it is small, it goes to zero. Our proofs rely on a graph-theoretic characterization of common knowledge that has independent interest
Deterministic Symmetry Breaking in Ring Networks
We study a distributed coordination mechanism for uniform agents located on a
circle. The agents perform their actions in synchronised rounds. At the
beginning of each round an agent chooses the direction of its movement from
clockwise, anticlockwise, or idle, and moves at unit speed during this round.
Agents are not allowed to overpass, i.e., when an agent collides with another
it instantly starts moving with the same speed in the opposite direction
(without exchanging any information with the other agent). However, at the end
of each round each agent has access to limited information regarding its
trajectory of movement during this round.
We assume that mobile agents are initially located on a circle unit
circumference at arbitrary but distinct positions unknown to other agents. The
agents are equipped with unique identifiers from a fixed range. The {\em
location discovery} task to be performed by each agent is to determine the
initial position of every other agent.
Our main result states that, if the only available information about movement
in a round is limited to %information about distance between the initial and
the final position, then there is a superlinear lower bound on time needed to
solve the location discovery problem. Interestingly, this result corresponds to
a combinatorial symmetry breaking problem, which might be of independent
interest. If, on the other hand, an agent has access to the distance to its
first collision with another agent in a round, we design an asymptotically
efficient and close to optimal solution for the location discovery problem.Comment: Conference version accepted to ICDCS 201
A Simple Approach to Error Reconciliation in Quantum Key Distribution
We discuss the error reconciliation phase in quantum key distribution (QKD)
and analyse a simple scheme in which blocks with bad parity (that is, blocks
containing an odd number of errors) are discarded. We predict the performance
of this scheme and show, using a simulation, that the prediction is accurate.Comment: 19 pages. Presented at the 53rd Annual Meeting of the Australian
Mathematical Society, Adelaide, Oct 1, 2009. See also
http://wwwmaths.anu.edu.au/~brent/pub/pub239.htm
Statistical Complexity and Nontrivial Collective Behavior in Electroencephalografic Signals
We calculate a measure of statistical complexity from the global dynamics of
electroencephalographic (EEG) signals from healthy subjects and epileptic
patients, and are able to stablish a criterion to characterize the collective
behavior in both groups of individuals. It is found that the collective
dynamics of EEG signals possess relative higher values of complexity for
healthy subjects in comparison to that for epileptic patients. To interpret
these results, we propose a model of a network of coupled chaotic maps where we
calculate the complexity as a function of a parameter and relate this measure
with the emergence of nontrivial collective behavior in the system. Our results
show that the presence of nontrivial collective behavior is associated to high
values of complexity; thus suggesting that similar dynamical collective process
may take place in the human brain. Our findings also suggest that epilepsy is a
degenerative illness related to the loss of complexity in the brain.Comment: 13 pages, 3 figure
Logical Omnipotence and Two notions of Implicit Belief
The most widespread models of rational reasoners (the model based on modal epistemic logic and the model based on probability theory) exhibit the problem of logical omniscience. The most common strategy for avoiding this problem is to interpret the models as describing the explicit beliefs of an ideal reasoner, but only the implicit beliefs of a real reasoner. I argue that this strategy faces serious normative issues. In this paper, I present the more fundamental problem of logical omnipotence, which highlights the normative content of the problem of logical omniscience. I introduce two developments of the notion of implicit belief (accessible and stable belief ) and use them in two versions of the most common strategy applied to the problem of logical omnipotence
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