# Process Discovery for Event Logs with Multi-Occurrence Event Types
## 1 Introduction  
The efficient management of the production and business processes has a high priority in every organization. The activities are composed into different workflows executed regularly to achieve the defined goals. The efficient workflow design and control has a special high importance in the case of the complex production processes of our days. Process mining is an umbrella term covering different activities related to workflow control. Process mining is used to discover, monitor, or improve processes and process models by extracting knowledge from the measured event logs. One of the key functionality fields is process discovery [1], which is used to build up the workflow process model from the available event logs. This tool is especially useful when the manual workflow schema construction is too expensive or impossible. In these cases, the automatic workflow schema induction provides a feasible and cost-effective solution. The generated workflow model can be used later, among others, for process automatization or conformance checking. According to the classification of the dominating business process-modelling tools presented in [PERSON] et al. [2], the main approaches in process modelling are as follows:  
* Automaton-based methods like Petri nets [3], IDEF [4], EPC (event-driven process chain) [5], and role activity diagrams [6];
* Data flow diagrams and value-stream mapping;
* Workflow modelling languages, like WPDL [7] and BPMN [8];
* Programming language-oriented methods, including unified modelling languages (UML). The Petri net model plays a key role as one of the oldest and most abstract models having many higher-level extensions. Regarding practical expressive power, the Business Process Model and Notation (BPMN) [9] is the dominating tool. These models usually support the XML languages as data interchange formats. One of the most powerful modelling languages is the YAWL language [10]. This model is the result of a systematic analysis by the Workflow Patterns Initiative [11] on the existing process modelling notations and workflow languages. In the practical applications, the workflow structure can be modelled with the following control elements:  
* Sequence: linear structure, where a task in a process can be executed after the completion of a preceding task;
* Branching (XOR): only one of the several outgoing paths is enabled;
* Fork (AND): the process path is split into two or more branches, which are activated concurrently;
* Split (OR): more or one of the several outgoing paths are enabled;
* Merging: synchronization of the several incoming threads. Process mining tools can be used also for performance analysis [12], where the process mining is used to automate finding or calculating the performance metrics. This solution provides faster, immediate feedback on the current process status. Another application field is conformance checking [13]. The engine compares the running or terminated processes with the given workflow model to discover differences and similarities between the model and event log. Most of the approaches perform the analysis on the complete terminated trace, which does not enable the prompt interaction of the control module. To enhance this important feature, current works focus on the development of on-line conformance analysis [14]. The fourth pillar of process mining is the model enhancement domain [15]. Having an existing workflow model, the enhancement module can manage dynamic workflow behavior; it can update the model with new elements and dependencies. In all components of process mining, the workflow model plays a central role. The manual construction of the model usually requires the cooperation of more experts, and it takes more time to finalize the model; thus, the manual model construction requires a high-cost investment. Driven by the requirements on cost-effective workflow model construction, the automatic workflow model discovery became a highly investigated research domain.