  Process models are, like event data, first-class citizens in most process
mining approaches. Several process modeling formalisms have been proposed and
used, e.g., Petri nets, BPMN, and process trees. Despite their frequent use,
little research addresses the formal properties of process trees and the
corresponding potential to improve the efficiency of solving common
computational problems. Therefore, in this paper, we propose an invertible
state space definition for process trees and demonstrate that the corresponding
state space graph is isomorphic to the state space graph of the tree's inverse.
Our result supports the development of novel, time-efficient, decomposition
strategies for applications of process trees. Our experiments confirm that our
state space definition allows for the adoption of bidirectional state space
search, which significantly improves the overall performance of state space
searches.
