  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.
