Uniform Sampling for Timed Automata with Application to Language Inclusion Measurement

Abstract

Monte Carlo model checking introduced by Smolka and Grosu is an approach to analyse non-probabilistic models using sampling and draw conclusions with a given confidence interval by applying statistical inference. Though not exhaustive, the method enables verification of complex models, even in cases where the underlying problem is undecidable. In this paper we develop Monte Carlo model checking techniques to evaluate quantitative properties of timed languages. Our approach is based on uniform random sampling of behaviours, as opposed to isotropic sampling that chooses the next step uniformly at random. The uniformity is defined with respect to volume measure of timed languages previously studied by Asarin, Basset and Degorre. We improve over their work by employing a zone graph abstraction instead of the region graph abstraction and incorporating uniform sampling within a zone-based Monte Carlo model checking framework. We implement our algorithms using tools PRISM, SageMath and COSMOS, and demonstrate their usefulness on statistical language inclusion measurement in terms of volume.

Generation of Signals Under Temporal Constraints for CPS Testing

“…The k th constraint is due to the guard x i ∈ (1, 6) (to be precise, with i = (k mod 4)+1) because the clock x i contains the sum of the 4 last delays before taking the k th transition. Computing the volume of such a timed polytope requires dynamic programming algorithms (involving an integral operator per transition) which can be found in [4,6].…”

“…2. For a given TA, our previous work [6] proposes a method for generating uniformly timed words of a given length. Such a uniform sampling is done by adding probability distributions on time delays along a run of the automaton.…”

“…For simplicity of presentation, we will explain only the generation of timed vectors in a timed polytope, or in a sequence of timed polytopes along a single path. Discrete branching can be handled similarly as in [6].…”

“…To address the first problem, we extend the method for uniform random generation of runs of timed automata [6] to propose a new method based on low discrepancy. The generated timed words are then mapped to input signals.…”

Integrating Simulink Models into the Model Checker Cosmos

“…Cosmos has been successfullly applied in the context of flexible manufacturing systems [2] and biological networks [3,6]. In addition, it has also been customised in order to address the challenges raised by different projects: simulation of rare events [7], cosimulation of a pacemaker software with a model of the human heart [8], sampling uniform trajectory for timed automata [5].…”