2 research outputs found
Distributional Probabilistic Model Checking
Probabilistic model checking can provide formal guarantees on the behavior of
stochastic models relating to a wide range of quantitative properties, such as
runtime, energy consumption or cost. But decision making is typically with
respect to the expected value of these quantities, which can mask important
aspects of the full probability distribution such as the possibility of
high-risk, low-probability events or multimodalities. We propose a
distributional extension of probabilistic model checking, applicable to
discrete-time Markov chains (DTMCs) and Markov decision processes (MDPs). We
formulate distributional queries, which can reason about a variety of
distributional measures, such as variance, value-at-risk or conditional
value-at-risk, for the accumulation of reward until a co-safe linear temporal
logic formula is satisfied. For DTMCs, we propose a method to compute the full
distribution to an arbitrary level of precision, based on a graph analysis and
forward analysis of the model. For MDPs, we approximate the optimal policy with
respect to expected value or conditional value-at-risk using distributional
value iteration. We implement our techniques and investigate their performance
and scalability across a range of benchmark models. Experimental results
demonstrate that our techniques can be successfully applied to check various
distributional properties of large probabilistic models.Comment: 20 pages, 2 pages appendix, 5 figures. Submitted for review. For
associated Github repository, see
https://github.com/davexparker/prism/tree/ing