Formal methods play an important role in testing and verifying software quality, especially in modern society with rapid technological updates. Learning-based techniques have been extensively applied to learn (a model or model-free) for formal verification and to learn system specifications, and resulted in numerous contributions. Due to the fact that adequate system models are often difficult to design manually and manual definition of specifications for such software systems gets infeasible, which motivate new research directions in learning models and/or specifications from observed system behaviors automatically. This paper mainly concentrates on learning-based techniques in formal methods area. An up-to-date overview of the current state-of-the-art in learning-based formal methods is provided in the paper. This paper is not a comprehensive survey of learning-based techniques in formal methods area, but rather as a survey of the taxonomy, applications and possible future directions in learning-based formal methods.
Probabilistic behavior is omnipresent in computer-controlled systems, in particular, so-called safety-critical hybrid systems, due to various reasons, like uncertain environments or fundamental properties of nature. In this paper, we extend the existing hybrid process algebra ACP[Formula: see text] with probability without sacrificing the nondeterministic choice operator. The existing approximate probabilistic bisimulation relation is fragile and not robust in the sense of being dependent on the deviation range of the transition probability. To overcome this defect, a novel approximate probabilistic bisimulation is proposed which is inspired by the idea of Probably Approximately Correct (PAC) by relaxing the constraints of transition probability deviation range. Traditional temporal logics, even probabilistic temporal logics, are expressive enough, but they are limited to producing only true or false responses, as they are still logics and not suitable for performance evaluation. To settle this problem, we present a new performance evaluation language that expands quantitative analysis from the value range of [Formula: see text] to real number to reason over probabilistic systems. After that, the corresponding algorithms for performance evaluation are given. Finally, an industrial example is given to demonstrate the effectiveness of our method.
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