Model Checking Markov Population Models by Stochastic Approximations

Luca Bortolussi; Roberta Lanciani; Laura Nenzi

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arXiv · 1711.03826

Model Checking Markov Population Models by Stochastic Approximations

Luca Bortolussi·Roberta Lanciani·Laura Nenzi

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Abstract

Many complex systems can be described by population models, in which a pool of agents interacts and produces complex collective behaviours. We consider the problem of verifying formal properties of the underlying mathematical representation of these models, which is a Continuous Time Markov Chain, often with a huge state space. To circumvent the state space explosion, we rely on stochastic approximation techniques, which replace the large model by a simpler one, guaranteed to be probabilistically consistent. We show how to efficiently and accurately verify properties of random individual agents, specified by Continuous Stochastic Logic extended with Timed Automata (CSL-TA), and how to lift these specifications to the collective level, approximating the number of agents satisfying them using second or higher order stochastic approximation techniques.

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Luca Bortolussi, Roberta Lanciani, Laura Nenzi. 2017-11-10. Model Checking Markov Population Models by Stochastic Approximations. https://arxiv.org/abs/1711.03826

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