Secret Protection in Labeled Petri Nets

2025-11-08

AI Summary

This paper investigates the Secret Protection Problem (SPP) in labeled Petri nets—ensuring, at minimal cost, that every executable path from the initial marking to any secret marking contains sufficiently many protected events. It introduces the first SPP framework for labeled Petri nets and rigorously distinguishes and formalizes two security mechanisms: Parikh-based (counting event multiplicities) and indicator-based (capturing event occurrence only). Methodologically, the work integrates Parikh vector analysis, path semantics modeling, and formal verification techniques. It establishes that both variants of SPP are ExpSpace-complete, thereby proving their decidability and precisely characterizing their theoretical complexity. This result provides the first tight complexity bound and foundational modeling framework for behaviorally grounded secret protection in discrete-event systems.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Natural Language Processing: Safety and Robustness
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We study the secret protection problem (SPP), where the objective is to find a policy of minimal cost ensuring that every execution path from an initial state to a secret state contains a sufficient number of protected events. The problem was originally introduced and studied in the setting of finite automata. In this paper, we extend the framework to labeled Petri nets. We consider two variants of the problem: the Parikh variant, where all occurrences of protected events along an execution path contribute to the security requirement, and the indicator variant, where each protected event is counted only once per execution path. We show that both variants can be solved in exponential space for labeled Petri nets, and that their decision versions are ExpSpace-complete. As a consequence, there is no polynomial-time or polynomial-space algorithm for these problems.

Problem

• Extends secret protection from finite automata to labeled Petri nets
• Solves minimal-cost policy for protecting execution paths to secrets
• Proves both problem variants are ExpSpace-complete with exponential space requirements

Innovation

• Secret protection in labeled Petri nets
• Parikh and indicator variants analyzed
• Exponential space complexity for solutions