Learning Probabilistic Automata for Model Checking

Abstract

Abstract-Obtaining accurate system models for verification is a hard and time consuming process, which is seen by industry as a hindrance to adopt otherwise powerful modeldriven development techniques and tools. In this paper we pursue an alternative approach where an accurate high-level model can be automatically constructed from observations of a given black-box embedded system. We adapt algorithms for learning finite probabilistic automata from observed system behaviors. We prove that in the limit of large sample sizes the learned model will be an accurate representation of the data-generating system. In particular, in the large sample limit, the learned model and the original system will define the same probabilities for linear temporal logic (LTL) properties. Thus, we can perform PLTL model-checking on the learned model to infer properties of the system. We perform experiments learning models from system observations at different levels of abstraction. The experimental results show the learned models provide very good approximations for relevant properties of the original system.

Faster Statistical Model Checking by Means of Abstraction and Learning

“…But, in addition, for the general case, this models is also providing good approximations for the initial (prefix) behavior of M a and hence preserve the probability of satisfaction for properties in the BLTL fragment (see Theorem 3 in [19]). Thereof, by using AAlergia or a similar learning algorithm, it holds that P r(M a |= ϕ) = P r(M ♯ |= ϕ) whenever ϕ belongs to BLTL.…”

“…In this paper, we use AAlergia [19] which is a state merging algorithm that exclusively learn deterministic models. Given a sample of traces, the algorithm proceeds in three steps.…”

“…It first builds an intermediate representation, a Frequency Prefix Tree Acceptor (FPTA), which is a restricted form of DPFA that represents all the traces in the input sample and their corresponding frequencies. Seconds, based on a compatibility criterion parametrized by α A (automatically computed, as explained in [19]), it iteratively merges states of the FPTA having the same labels and similar probability distributions until reaching a compact DPFA. Finally, it transforms the obtained DPFA into a DLMC model.…”

“…AAlergia is proven to converge to the correct model in the limit [19] if the input traces are generated, with random lengths, from an LMC model. A first consequence concerns verification on DLMCs and ensures that, in the limit (with sufficiently big sample set of traces), a given LTL property will hold on the original and the learned model with the same probability.…”

“…Third, the set of projected traces is used as an input to a learning algorithm. For experiments, we have used AAlergia [19], however, any other algorithm could be used. The output of the learning denoted M ♯ on Figure 2 will be used to evaluate the property of interest ϕ.…”