Distributional Probabilistic Model Checking

TL;DR

This paper extends probabilistic model checking to analyze entire probability distributions of outcomes, enabling assessment of risks and multimodal behaviors in stochastic models like DTMCs and MDPs.

Contribution

It introduces a distributional extension for probabilistic model checking, including methods for computing full distributions and approximating optimal policies for distributional measures.

Findings

Effective computation of full distributions for DTMCs.

Approximate optimal policies for MDPs with respect to distributional measures.

Scalability demonstrated on large benchmark models.

Abstract

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.