The execution logs that are used for process mining in practice are often obtained by querying an operational database and storing the result in a flat file. Consequently, the data processing power of the database system cannot be used anymore for this information, leading to constrained flexibility in the definition of mining patterns and limited execution performance in mining large logs. Enabling process mining directly on a database - instead of via intermediate storage in a flat file - therefore provides additional flexibility and efficiency. To help facilitate this ideal of in-database process mining, this paper formally defines a database operator that extracts the 'directly follows' relation from an operational database. This operator can both be used to do in-database process mining and to flexibly evaluate process mining related queries, such as: "which employee most frequently changes the 'amount' attribute of a case from one task to the next". We define the operator using the well-known relational algebra that forms the formal underpinning of relational databases. We formally prove equivalence properties of the operator that are useful for query optimization and present time-complexity properties of the operator. By doing so this paper formally defines the necessary relational algebraic elements of a 'directly follows' operator, which are required for implementation of such an operator in a DBMS.
Enterprise information systems support and control operational business processes ranging from simple internal back-office process to complex interorganizational processes. Technologies such as workflow management (WFM), enterprise, application integration (EAI), enterprise resource planning (ERP), and web services (WS) typically focus on the realization of IT support rather than monitoring the operational business processes. Process mining aims at extracting information from event logs to capture the business process as it is being executed. In this paper, we put the topic of process mining into context, discuss the main issues around process mining, and finally we introduce the papers in this special issue.  Process mining techniques often reveal that real-life processes are more variable than anticipated. Although declarative process models are more suitable for less structured processes, most discovery techniques generate conventional procedural models. In this paper, we focus on discovering Declare models based on event logs. A Declare model is composed of temporal constraints. Despite the suitability of declarative process models for less structured processes, their discovery is far from trivial. Even for smaller processes there are many potential constraints. Moreover, there may be many constraints that are trivially true and that do not characterize the process well. Naively checking all possible constraints is computationally intractable and may lead to models with an excessive number of constraints. Therefore, we have developed an Apriori algorithm to reduce the search space. Moreover, we use new metrics to prune the model. As a result, we can quickly generate understandable Declare models for real-life event logs.