Exploring Complexity: An Extended Study of Formal Properties for Process Model Complexity Measures

TL;DR

This paper extends Weyuker's formal properties to the domain of process-model complexity measures by adapting and analyzing a broad set of measures on labeled workflow nets. It defines and evaluates a comprehensive suite of measures across established and newly introduced properties, including extensions like DEF, INF, MIN, ADD, MON, and PERM, and systematically applies them to dimensions such as Token Behavior and Path Complexity. The key contribution is a rigorous, property-driven assessment that clarifies which measures are normative versus descriptive and provides practical guidance for analysts and algorithm designers in selecting measures that align with their goals. The findings enhance understanding of how complexity measures influence process discovery and evaluation, with implications for method selection and future research on more expressive or domain-tailored metrics.

Abstract

A good process model is expected not only to reflect the behavior of the process, but also to be as easy to read and understand as possible. Because preferences vary across different applications, numerous measures provide ways to reflect the complexity of a model with a numeric score. However, this abundance of different complexity measures makes it difficult to select one for analysis. Furthermore, most complexity measures are defined for BPMN or EPC, but not for workflow nets. This paper is an extended analysis of complexity measures and their formal properties. It adapts existing complexity measures to the world of workflow nets. It then compares these measures with a set of properties originally defined for software complexity, as well as new extensions to it. We discuss the importance of the properties in theory by evaluating whether matured complexity measures should fulfill them or whether they are optional. We find that not all inspected properties are mandatory, but also demonstrate that the behavior of evolutionary process discovery algorithms is influenced by some of these properties. Our findings help analysts to choose the right complexity measure for their use-case.

Figures (21)

• Figure 1: A workflow net $M$ with $14$ places and $11$ transitions.
• Figure 2: The smallest possible workflow net, $W_0$.
• Figure 3: A schematic overview of the four operations of Definition \ref{['def:operations']}.
• Figure 4: Three simple workflow nets, $W_1^{\text{size}}, W_2^{\text{size}}, W_3^{\text{size}}$, with complexity scores $C_{\text{size}}(W_1^{\text{size}}) = 3$ and $C_{\text{size}}(W_2^{\text{size}}) = C_{\text{size}}(W_3^{\text{size}}) = 5$.
• Figure 6: Three simple workflow nets, $W_1^{\text{MM}}, W_2^{\text{MM}}, W_3^{\text{MM}}$, with complexity scores $C_{\text{MM}}(W_1^{\text{MM}}) = 0$ and $C_{\text{MM}}(W_2^{\text{MM}}) = C_{\text{MM}}(W_3^{\text{MM}}) = 4$.

Theorems & Definitions (9)

• definition \@thmcounterdefinition: Petri net
• definition \@thmcounterdefinition: Labeled workflow nets
• definition \@thmcounterdefinition: Connectors in workflow nets
• definition \@thmcounterdefinition: Relabeling of a Workflow net
• definition \@thmcounterdefinition: Permutations of Workflow Nets
• definition \@thmcounterdefinition: Operations on workflow nets
• definition \@thmcounterdefinition: Complexity Measure
• theorem \@thmcountertheorem
• proof