Benoît Delahaye

Statistical model checking: an overview

Quantitative properties of stochastic systems are usually specified in logics that allow one to compare the measure of executions satisfying certain temporal properties with thresholds. The model checking problem for stochastic systems with respect to such logics is typically solved by a numerical approach [31,8,35,22,21,5] that iteratively computes (or approximates) the exact measure of paths satisfying relevant subformulas; the algorithms themselves depend on the class of systems being analyzed as well as the logic used for specifying the properties. Another approach to solve the model checking problem is to simulate the system for finitely many executions, and use hypothesis testing to infer whether the samples provide a statistical evidence for the satisfaction or violation of the specification. In this tutorial, we survey the statistical approach, and outline its main advantages in terms of efficiency, uniformity, and simplicity.

Abstract probabilistic automata

Probabilistic Automata (PAs) are a widely-recognized mathematical framework for the specification and analysis of systems with non-deterministic and stochastic behaviors. This paper proposes Abstract Probabilistic Automata (APAs), that is a novel abstraction model for PAs. In APAs uncertainty of the non-deterministic choices is modeled by may/must modalities on transitions while uncertainty of the stochastic behaviour is expressed by (underspecified) stochastic constraints. We have developed a complete abstraction theory for PAs, and also propose the first specification theory for them. Our theory supports both satisfaction and refinement operators, together with classical stepwise design operators. In addition, we study the link between specification theories and abstraction in avoiding the state-space explosion problem.

Constraint Markov chains

Notions of specification, implementation, satisfaction, and refinement, together with operators supporting stepwise design, constitute a specification theory. We construct such a theory for Markov Chains (MCs) employing a new abstraction of a Constraint MC. Constraint MCs permit rich constraints on probability distributions and thus generalize prior abstractions such as Interval MCs. Linear (polynomial) constraints suffice for closure under conjunction (respectively parallel composition). This is the first specification theory for MCs with such closure properties. We discuss its relation to simpler operators for known languages such as probabilistic process algebra. Despite the generality, all operators and relations are computable.

Compositional Design Methodology with Constraint Markov Chains

Notions of specification, implementation, satisfaction, and refinement, together with operators supporting stepwise design, constitute a {specification theory}. We construct such a theory for Markov Chains (MCs) employing a new abstraction of a Constraint MC. Constraint MCs permit rich constraints on probability distributions and thus generalize prior abstractions such as Interval MCs. Linear (polynomial) constraints suffice for closure under conjunction (respectively parallel composition). This is the first specification theory for MCs with such closure properties. We discuss its relation to simpler operators for known languages such as probabilistic process algebra. Despite the generality, all operators and relations are computable.

Statistical abstraction and model-checking of large heterogeneous systems

We propose a new simulation-based technique for verifying applications running within a large heterogeneous system. Our technique starts by performing simulations of the system in order to learn the context in which the application is used. Then, it creates a stochastic abstraction for the application, which takes the context information into account. This smaller model can be verified using efficient techniques such as statistical model checking. We have applied our technique to an industrial case study: the cabin communication system of an airplane. We use the BIP toolset to model and simulate the system. We have conducted experiments to verify the clock synchronization protocol i.e., the application used to synchronize the clocks of all computing devices within the system.

Statistical model checking qos properties of systems with SBIP

BIP is a component-based framework supporting rigorous design of embedded systems. This paper presents SBIP, an extension of BIP that relies on a new stochastic semantics that enables verification of large-size systems by using Statistical Model Checking. The approach is illustrated on several industrial case studies.

Probabilistic contracts: a compositional reasoning methodology for the design of systems with stochastic and/or non-deterministic aspects

A contract allows to distinguish hypotheses made on a system (the guarantees) from those made on its environment (the assumptions). In this paper, we focus on models of Assume/Guarantee contracts for (stochastic) systems. We consider contracts capable of capturing reliability and availability properties of such systems. We also show that classical notions of Satisfaction and Refinement can be checked by effective methods thanks to a reduction to classical verification problems. Finally, theorems supporting compositional reasoning and enabling the scalable analysis of complex systems are also studied.

Probabilistic Contracts: A Compositional Reasoning Methodology for the Design of Stochastic Systems

A contract allows to distinguish hypotheses made on a system (the guarantees) from those made on its environment (the assumptions). In this paper, we focus on models of Assume/Guarantee contracts for (stochastic) systems. We consider contracts capable of capturing reliability and availability properties of such systems. We also show that classical notions of Satisfaction and Refinement can be checked by effective methods thanks to a reduction to classical verification problems. Finally, theorems supporting compositional reasoning and enabling the scalable analysis of complex systems are also studied.

Decision problems for interval Markov chains

Interval Markov Chains (IMCs) are the base of a classic probabilistic specification theory by Larsen and Jonsson in 1991. They are also a popular abstraction for probabilistic systems. In this paper we study complexity of several problems for this abstraction, that stem from compositional modeling methodologies. In particular we close the complexity gap for thorough refinement of two IMCs and for deciding the existence of a common implementation for an unbounded number of IMCs, showing that these problems are EXPTIME-complete. We also prove that deciding consistency of an IMC is polynomial and discuss suitable notions of determinism for such specifications.

New Results on Abstract Probabilistic Automata

Probabilistic Automata (PAs) are a recognized framework for modeling and analysis of nondeterministic systems with stochastic behavior. Recently, we proposed Abstract Probabilistic Automata (APAs) -- an abstraction framework for PAs. In this paper, we discuss APAs over dissimilar alphabets, a determinisation operator, conjunction of non-deterministic APAs, and an APA-embedding of Interface Automata. We conclude introducing a tool for automatic manipulation of APAs.