13,926 research outputs found
Learning deterministic probabilistic automata from a model checking perspective
Probabilistic automata models play an important role in the formal design and analysis of hard- and software systems. In this area of applications, one is often interested in formal model-checking procedures for verifying critical system properties. Since adequate system models are often difficult to design manually, we are interested in learning models from observed system behaviors. To this end we adopt techniques for learning finite probabilistic automata, notably the Alergia algorithm. In this paper we show how to extend the basic algorithm to also learn automata models for both reactive and timed systems. A key question of our investigation is to what extent one can expect a learned model to be a good approximation for the kind of probabilistic properties one wants to verify by model checking. We establish theoretical convergence properties for the learning algorithm as well as for probability estimates of system properties expressed in linear time temporal logic and linear continuous stochastic logic. We empirically compare the learning algorithm with statistical model checking and demonstrate the feasibility of the approach for practical system verification
Convergence in Models with Bounded Expected Relative Hazard Rates
We provide a general framework to study stochastic sequences related to
individual learning in economics, learning automata in computer sciences,
social learning in marketing, and other applications. More precisely, we study
the asymptotic properties of a class of stochastic sequences that take values
in and satisfy a property called "bounded expected relative hazard
rates." Sequences that satisfy this property and feature "small step-size" or
"shrinking step-size" converge to 1 with high probability or almost surely,
respectively. These convergence results yield conditions for the learning
models in B\"orgers, Morales, and Sarin (2004), Erev and Roth (1998), and
Schlag (1998) to choose expected payoff maximizing actions with probability one
in the long run.Comment: After revision. Accepted for publication by Journal of Economic
Theor
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
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