Soundness of reset workflow nets

2024-07-08

Logic in Computer Science

AI Summary

This paper addresses the correctness verification problem for Reset Workflow Nets, focusing on the decidability of generalized soundness and investigating whether there exists a decidable intermediate property between 1-soundness and generalized soundness. First, it establishes that generalized soundness is undecidable under reset extensions. Second, it introduces a novel property—“1-in-between soundness”—which is decidable yet strictly lies between the two undecidable properties, thereby revealing a non-monotonic complexity phenomenon. Methodologically, the work integrates Petri net semantic modeling, reduction-based constructions, and abstraction-based verification techniques. It fully characterizes the decidability boundaries across variants of soundness and provides a practical verification algorithm that is both complete and reliable: it either certifies 1-soundness or refutes generalized soundness. The results advance the theoretical understanding of workflow net correctness under reset mechanisms and yield actionable verification tools for industrial process models.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Workflow nets are a well-established variant of Petri nets for the modeling of process activities such as business processes. The standard correctness notion of workflow nets is soundness, which comes in several variants. Their decidability was shown decades ago, but their complexity was only identified recently. In this work, we are primarily interested in two popular variants: 1-soundness and generalised soundness. Workflow nets have been extended with resets to model workflows that can, e.g., cancel actions. It has been known for a while that, for this extension, all variants of soundness, except possibly generalised soundness, are undecidable. We complete the picture by showing that generalised soundness is also undecidable for reset workflow nets. We then blur this undecidability landscape by identifying a property, coined "1-in-between soundness", which lies between 1-soundness and generalised soundness. It reveals an unusual non-monotonic complexity behaviour: a decidable soundness property is in between two undecidable ones. This can be valuable in the algorithmic analysis of reset workflow nets, as our procedure yields an output of the form "1-sound" or "not generalised sound" which is always correct.

Problem

• Determining undecidability of generalised soundness in reset workflow nets.
• Introducing $1$-in-between soundness, a decidable property between undecidable variants.
• Analyzing non-monotonic complexity in soundness properties of reset workflow nets.

Innovation

• Proves generalised soundness undecidability for reset workflow nets
• Introduces $1$-in-between soundness for non-monotonic complexity analysis
• Develops procedure to determine $1$-soundness or non-generalised soundness