Recently, formal methods have gained significant traction for describing, checking, and synthesizing the behaviors of cyber-physical systems. Among these methods, temporal logics stand out as they offer concise mathematical formulas to express desired system properties. In this thesis, our focus revolves around two primary applications of temporal logics in describing the behavior of autonomous system. The first involves integrating temporal logics with machine learning techniques to deduce a temporal logic specification based on the system's execution traces. The second application concerns using temporal logics to define traffic rules and develop a control scheme that guarantees compliance with these rules for autonomous vehicles. Ultimately, our objective is to combine these approaches, infer a specification that characterizes the desired behaviors of autonomous vehicles, and ensure that these behaviors are upheld during runtime. In the first study of this thesis, our focus is on learning Signal Temporal Logic (STL) specifications from system execution traces. Our approach involves two main phases. Initially, we address an offline supervised learning problem, leveraging the availability of system traces and their corresponding labels. Subsequently, we introduce a time-incremental learning framework. This framework is designed for a dataset containing labeled signal traces with a common time horizon. It provides a method to predict the label of a signal as it is received incrementally over time. To tackle both problems, we propose two decision tree-based approaches, with the aim of enhancing the interpretability and classification performance of existing methods. The simulation results demonstrate the efficiency of our proposed approaches. In the next study, we address the challenge of guaranteeing compliance with traffic rules expressed as STL specifications within the domain of autonomous driving. Our focus is on developing control frameworks for a fully autonomous vehicle operating in a deterministic or stochastic environment. Our frameworks effectively translate the traffic rules into high-level decisions and accomplish low-level vehicle control with good real-time performance. Compared to existing literature, our approaches demonstrate significant enhancements in terms of runtime performance. / 2025-01-17T00:00:00Z