An Invertible State Space for Process Trees

TL;DR

This paper introduces an invertible state space model for process trees, enabling bidirectional search strategies that enhance the efficiency of process mining tasks.

Contribution

It proposes a novel invertible state space formalism for process trees, facilitating more efficient decomposition and search algorithms in process mining.

Findings

Bidirectional state space search significantly improves performance.

The state space graph is isomorphic to the inverse process.

Supports development of time-efficient process analysis methods.

Abstract

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.