8,975 research outputs found
Probabilistic Bisimulation: Naturally on Distributions
In contrast to the usual understanding of probabilistic systems as stochastic
processes, recently these systems have also been regarded as transformers of
probabilities. In this paper, we give a natural definition of strong
bisimulation for probabilistic systems corresponding to this view that treats
probability distributions as first-class citizens. Our definition applies in
the same way to discrete systems as well as to systems with uncountable state
and action spaces. Several examples demonstrate that our definition refines the
understanding of behavioural equivalences of probabilistic systems. In
particular, it solves a long-standing open problem concerning the
representation of memoryless continuous time by memory-full continuous time.
Finally, we give algorithms for computing this bisimulation not only for finite
but also for classes of uncountably infinite systems
Basic Ideas to Approach Metastability in Probabilistic Cellular Automata
Cellular Automata are discrete--time dynamical systems on a spatially
extended discrete space which provide paradigmatic examples of nonlinear
phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular
Automata, are discrete time Markov chains on lattice with finite single--cell
states whose distinguishing feature is the \textit{parallel} character of the
updating rule. We review some of the results obtained about the metastable
behavior of Probabilistic Cellular Automata and we try to point out
difficulties and peculiarities with respect to standard Statistical Mechanics
Lattice models.Comment: arXiv admin note: text overlap with arXiv:1307.823
A guided tour of asynchronous cellular automata
Research on asynchronous cellular automata has received a great amount of
attention these last years and has turned to a thriving field. We survey the
recent research that has been carried out on this topic and present a wide
state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat
In Defense of DEFECT or Cooperation does not Justify the Solution Concept
The one-state machine that always defects is the only evolutionarily stable strategy in the machine game that is derived from the prisoners' dilemma, when preferences are lexicographic in the complexity. This machine is the only stochastically stable strategy of the machine game when players are restricted to choosing machines with a uniformly bounded complexity.Cooperation; prisoners' dilemma; automata; evolution.
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