An expectation transformer approach to predicate abstraction and data independence for probabilistic programs

In this paper we revisit the well-known technique of predicate abstraction to characterise performance attributes of system models incorporating probability. We recast the theory using expectation transformers, and identify transformer properties which correspond to abstractions that yield nevertheless exact bound on the performance of infinite state probabilistic systems. In addition, we extend the developed technique to the special case of "data independent" programs incorporating probability. Finally, we demonstrate the subtleness of the extended technique by using the PRISM model checking tool to analyse an infinite state protocol, obtaining exact bounds on its performance

Strategy Synthesis for Autonomous Agents Using PRISM

We present probabilistic models for autonomous agent search and retrieve missions derived from Simulink models for an Unmanned Aerial Vehicle (UAV) and show how probabilistic model checking and the probabilistic model checker PRISM can be used for optimal controller generation. We introduce a sequence of scenarios relevant to UAVs and other autonomous agents such as underwater and ground vehicles. For each scenario we demonstrate how it can be modelled using the PRISM language, give model checking statistics and present the synthesised optimal controllers. We conclude with a discussion of the limitations when using probabilistic model checking and PRISM in this context and what steps can be taken to overcome them. In addition, we consider how the controllers can be returned to the UAV and adapted for use on larger search areas

Local abstraction refinement for probabilistic timed programs

We consider models of programs that incorporate probability, dense real-time and data. We present a new abstraction refinement method for computing minimum and maximum reachability probabilities for such models. Our approach uses strictly local refinement steps to reduce both the size of abstractions generated and the complexity of operations needed, in comparison to previous approaches of this kind. We implement the techniques and evaluate them on a selection of large case studies, including some infinite-state probabilistic real-time models, demonstrating improvements over existing tools in several cases

On Quantitative Software Verification

International audienceSoftware verification has made great progress in recent years, resulting in several tools capable of working directly from source code, for example, SLAM and Astree. Typical properties that can be verified are expressed as Boolean assertions or temporal logic properties, and include whether the program eventually terminates, or the executions never violate a safety property. The underlying techniques crucially rely on the ability to extract from programs, using compiler tools and predicate abstraction, finite-state abstract models, which are then iteratively refined to either demonstrate the violation of a safety property (e.g. a buffer overflow) or guarantee the absence of such faults. An established method to achieve this automatically executes an abstraction-refinement loop guided by counterexample traces [1]

PrIC3: Property Directed Reachability for MDPs

IC3 has been a leap forward in symbolic model checking. This paper proposes PrIC3 (pronounced pricy-three), a conservative extension of IC3 to symbolic model checking of MDPs. Our main focus is to develop the theory underlying PrIC3. Alongside, we present a first implementation of PrIC3 including the key ingredients from IC3 such as generalization, repushing, and propagation

Model Checking Finite-Horizon Markov Chains with Probabilistic Inference

We revisit the symbolic verification of Markov chains with respect to finite horizon reachability properties. The prevalent approach iteratively computes step-bounded state reachability probabilities. By contrast, recent advances in probabilistic inference suggest symbolically representing all horizon-length paths through the Markov chain. We ask whether this perspective advances the state-of-the-art in probabilistic model checking. First, we formally describe both approaches in order to highlight their key differences. Then, using these insights we develop Rubicon, a tool that transpiles Prism models to the probabilistic inference tool Dice. Finally, we demonstrate better scalability compared to probabilistic model checkers on selected benchmarks. All together, our results suggest that probabilistic inference is a valuable addition to the probabilistic model checking portfolio -- with Rubicon as a first step towards integrating both perspectives.Comment: Technical Report. Accepted at CAV 202