Probabilistic Black-Box Checking via Active MDP Learning

TL;DR

This paper presents ProbBBC, an advanced black-box testing method for stochastic systems that combines active MDP learning, probabilistic model checking, and statistical testing to improve efficiency and accuracy.

Contribution

It introduces a novel integrated approach for stochastic black-box testing that enhances traditional methods with active MDP learning and probabilistic verification.

Findings

ProbBBC outperforms existing methods on systems with limited observations.

The integrated approach improves testing efficiency and accuracy.

Experimental results validate the effectiveness of the proposed method.

Abstract

We introduce a novel methodology for testing stochastic black-box systems, frequently encountered in embedded systems. Our approach enhances the established black-box checking (BBC) technique to address stochastic behavior. Traditional BBC primarily involves iteratively identifying an input that breaches the system's specifications by executing the following three phases: the learning phase to construct an automaton approximating the black box's behavior, the synthesis phase to identify a candidate counterexample from the learned automaton, and the validation phase to validate the obtained candidate counterexample and the learned automaton against the original black-box system. Our method, ProbBBC, refines the conventional BBC approach by (1) employing an active Markov Decision Process (MDP) learning method during the learning phase, (2) incorporating probabilistic model checking in the synthesis phase, and (3) applying statistical hypothesis testing in the validation phase. ProbBBC uniquely integrates these techniques rather than merely substituting each method in the traditional BBC; for instance, the statistical hypothesis testing and the MDP learning procedure exchange information regarding the black-box system's observation with one another. The experiment results suggest that ProbBBC outperforms an existing method, especially for systems with limited observation.