Computing Alignments for Partially-ordered Traces Through Petri Net Unfoldings

TL;DR

An improved approach to conformance checking based upon partially ordered event data by utilizing Petri net unfolding, which leverages partial-order semantics of Petri nets to represent concurrency and uncertainty in event logs more effectively is proposed.

Abstract

Conformance checking techniques aim to provide diagnostics on the conformity between process models and event data. Conventional methods, such as trace alignments, assume strict total ordering of events, leading to inaccuracies when timestamps are overlapping, coarse, or missing. In contrast, existing methods that support partially ordered events rely upon the interleaving semantics of Petri nets, the reachability graphs, which suffer from the state space explosion problem. %Besides, this view also forces the solution to create a partially ordered alignment almost artificially. This paper proposes an improved approach to conformance checking based upon partially ordered event data by utilizing Petri net unfolding, which leverages partial-order semantics of Petri nets to represent concurrency and uncertainty in event logs more effectively. Unlike existing methods, our approach offers a streamlined one-step solution, improving efficiency in the computation of alignments. Additionally, we introduce a novel visualization technique for partially ordered unfolding-based alignments. We implement unfolding-based alignments with its user-friendly insights in a conformance analysis tool. Our experimental evaluation, conducted on synthetic and real-world event logs, demonstrates that the unfolding-based approach is particularly robust in handling high degrees of parallelism and complexity in process models.

Figures (11)

• Figure 1: An example Petri net $\mathcal{N}_{mgmt}$ of a software development management process with the initial marking $M_{init} = [p_0]$ and final marking $M_{final}=[p_{10}]$
• Figure 2: A system net $\mathcal{N}$ (left) with $M_{init}=[a,b,c]$, $M_{final}=[d,c,e]$, and its branching processes $\beta$ (right), which is also a complete finite prefix of the unfolding of $\mathcal{N}$.
• Figure 3: Overview of the proposed method to compute unfolding-based alignments given a partially-ordered trace and a process model. Input and output of each step are shown through dashed arrows. Various steps are highlighted in blue
• Figure 4: An example of a u-alignment along with its corresponding alignment order
• Figure 5: An extended synchronous product net $SN_{\otimes}^{ext}$ of an SPN of a trace net and a model net. The target transition is $t^*$, and a target place $p^*$ is a successor to $t^*$. For this system net, $M_{init,ext}=[p_{(\blacktriangleright,b)},p_0]$ and $M_{final,ext}=[p^*]$

Theorems & Definitions (17)

• definition thmcounterdefinition: Partially-ordered Trace (P-Trace)
• definition thmcounterdefinition: Labeled Petri Net, System Net
• definition thmcounterdefinition: Pre- and Postset
• definition thmcounterdefinition: Occurrence Net, Causal Net
• definition thmcounterdefinition: Branching Process
• definition thmcounterdefinition: Local Configuration
• definition thmcounterdefinition: Local Distributed Run
• definition thmcounterdefinition: Unfolding-based Alignment (u-alignment)
• definition thmcounterdefinition: Extended Synchronous Product Net
• definition thmcounterdefinition: Alignment Run