This paper presents three methods for discovering formal models of software processes from event-based data. The methods are based on grammar inference and are designed to automatically derive a formal model of a process from event data collected during process execution. The three methods range from purely algorithmic to purely statistical. The first method, RNet, is a statistical approach that uses a neural network to infer a finite-state machine (FSM) model of the process. The second method, Ktail, is an algorithmic approach that uses a prefix tree to infer an FSM model. The third method, Markov, is a hybrid approach that combines algorithmic and statistical techniques to infer an FSM model. The paper discusses the challenges of discovering formal models of software processes, particularly the difficulty of developing a formal model for an ongoing, complex process. It also discusses the importance of using event-based data to model software processes, as event data can capture the dynamic behavior of a process in terms of identifiable, instantaneous actions. The paper also discusses the limitations of grammar inference methods, including the inability to model concurrency and the difficulty of inferring models from positive samples alone. The paper presents a framework for process discovery based on event-based data. It describes the three methods in detail, including their implementation and application in an industrial case study. The paper also discusses the theoretical complexities of grammar inference and the practical challenges of applying these methods to real-world software processes. The paper concludes with a discussion of the future work in this area, including the need for further research on the application of grammar inference methods to software processes and the potential for extending these methods to other types of processes and behaviors.This paper presents three methods for discovering formal models of software processes from event-based data. The methods are based on grammar inference and are designed to automatically derive a formal model of a process from event data collected during process execution. The three methods range from purely algorithmic to purely statistical. The first method, RNet, is a statistical approach that uses a neural network to infer a finite-state machine (FSM) model of the process. The second method, Ktail, is an algorithmic approach that uses a prefix tree to infer an FSM model. The third method, Markov, is a hybrid approach that combines algorithmic and statistical techniques to infer an FSM model. The paper discusses the challenges of discovering formal models of software processes, particularly the difficulty of developing a formal model for an ongoing, complex process. It also discusses the importance of using event-based data to model software processes, as event data can capture the dynamic behavior of a process in terms of identifiable, instantaneous actions. The paper also discusses the limitations of grammar inference methods, including the inability to model concurrency and the difficulty of inferring models from positive samples alone. The paper presents a framework for process discovery based on event-based data. It describes the three methods in detail, including their implementation and application in an industrial case study. The paper also discusses the theoretical complexities of grammar inference and the practical challenges of applying these methods to real-world software processes. The paper concludes with a discussion of the future work in this area, including the need for further research on the application of grammar inference methods to software processes and the potential for extending these methods to other types of processes and behaviors.