Research on <i>k</i>-Step Active Opacity of Stochastic Discrete Event Systems

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Research on k-Step Active Opacity of Stochastic Discrete Event Systems

更新时间：2026-05-27

- Research on k-Step Active Opacity of Stochastic Discrete Event Systems
- Vol. 42, Issue 4, Pages: 79-87(2025)
- 作者机构：
  
  广东工业大学计算机学院,广东,广州,510006
- 作者简介：
- 基金信息：
- DOI：10.12052/gdutxb.240131
  CLC： TP309
- Published：2025
- 稿件说明：
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刘伟奇, 刘富春. 随机离散事件系统的k步主动不透明性研究[J]. 广东工业大学学报, 2025, 42(4): 79–87.

Liu Weiqi, Liu Fuchun. Research on k-Step Active Opacity of Stochastic Discrete Event Systems[J]. 2025, 42(4): 79-87. DOI: 10.12052/gdutxb.240131.
刘伟奇, 刘富春. 随机离散事件系统的k步主动不透明性研究[J]. 广东工业大学学报, 2025, 42(4): 79–87. DOI： 10.12052/gdutxb.240131

Liu Weiqi, Liu Fuchun. Research on k-Step Active Opacity of Stochastic Discrete Event Systems[J]. 2025, 42(4): 79-87. DOI: 10.12052/gdutxb.240131. DOI：

摘要

近年来，由于离散事件系统的不透明性在信息安全机制中取得了许多应用成果，引起了国内外众多学者的广泛关注。本文基于随机离散事件系统框架，针对系统存在泄密路径的安全问题，提出了通过主动控制增强系统

$ k $

<

img text_id='M3' class='formula-img' style='display:none;' src='240131_M3.jpg'>

步不透明性的方法，确保系统中所有秘密状态均不被泄露。首先，对随机离散事件系统的

$ k $

<

img text_id='M3' class='formula-img' style='display:none;' src='240131_M3.jpg'>

步主动不透明性进行形式化。其次，通过构造

$ k $

<

img text_id='M3' class='formula-img' style='display:none;' src='240131_M3.jpg'>

步主动不透明性验证器，为系统中每个秘密状态找到一个泄密概率最低的可控事件串，使系统可以通过强制执行可控事件以最安全的路径进入秘密状态，以达到增强

$ k $

<

img text_id='M3' class='formula-img' style='display:none;' src='240131_M3.jpg'>

步不透明性的目的。此外，也得到一个随机离散事件系统

$ k $

<

img text_id='M3

' class='formula-img' style='display:none;' src='240131_M3.jpg'>

步主动不透明性的充分必要条件，可用于验证随机离散事件系统的

$ k $

<

img text_id='M3' class='formula-img' style='display:none;' src='240131_M3.jpg'>

步主动不透明性。

Abstract

In recent years

the opacity of discrete event systems has achieved remarkable application results in information security mechanisms

attracting increasing attention from the researchers of the world. With the aim to address the security issue of leakage paths in the system

this paper proposes a method to enhance the

$ k $

<

img text_id='M9' class='formula-img' style='display:none;' src='240131_M9.jpg'>

-step opacity of the system through active control based on the framework of stochastic discrete event systems

ensuring that all secret states in the system are not disclosed. First

the

$ k $

<

img text_id='M9' class='formula-img' style='display:none;' src='240131_M9.jpg'>

-step active opacity of stochastic discrete event systems is formalized. Second

by constructing a

$ k $

<

img text_id='M9' class='formula-img' style='display:none;' src='240131_M9.jpg'>

-step active opacity verifier

a controllable event string with the lowest leakage probability is found for each secret state in the system

allowing the system to enter the secret state through the safest path by enforcing controllable events. In this way

the

$ k $

<

img text_id='M9' class='formula-img' style='display:none;' src='240131_M9.jpg'>

-step opacity can be enhanced

and additionally a necessary and sufficient condition for the

$ k $

<

img text_id='M9' class='formula-img' style='display:none;' src='240131_M9.jpg'>

-step active opacity of stochastic discrete event systems is obtained

which can be used to verify the

$ k $

<

img text_id='M9' class='formula-img' style='display:none;' src='240131_M9.jpg'>

-step active opacity of stochastic discrete event systems.

关键词

Keywords

references

CASSANDRAS C G, LAFORTUNE S. Introduction to discrete event systems[M]. 2nd ed. New York: Springer, 2008, 35-48.

WANG X Y, OUYANG D T, ZHAO J. Discrete-event system diagnosis upon incomplete model[J]. Journal of Software, 2012, 23(3): 465-475.

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MARKOVSKI J. Towards optimal supervisory control of discrete-time stochastic discrete-event processes with data[C]. IEEE 13th International Conference on Application of Concurrency to System Design. Barcelona: IEEE, 2013: 31-40.

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BASILE F, TOMMASI G D, MOTTA C. et al, Necessary and sufficient condition to assess initial-state-opacity in live bounded and reversible discrete event systems[J]. IEEE Control Systems Letters, 2022, 6: 2683-2688.

DONG Y, LI Z, WU N. Symbolic verification of current-state opacity of discrete event systems using Petri nets[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2022, 52(12): 7628-7641.

LIU F C, ZHANG X, ZHAO R. The current state opacity of incomplete discrete event systems[J]. Control Theory Applications, 2019, 36(7): 1067-1071.

TAN J X, LIU F, ZBIGNIEW D. Active opacity of discrete-event systems[J]. International Journal of Control, 2023, 96(8): 2090-2099.

LIAN Y H, LIU F C. Research on active opacity of fuzzy discrete event systems[J]. Journal of Guangdong University of Technology, 2025, 42(1): 126-133.

SABOORI A, HADJICOSTIS C N. Verification of k -step opacity and analysis of its complexity[J ] . IEEE Tr ansactions on Automation Science and Engineering, 2011, 8(3): 549-559.

SABOORI A. Verification of infinite-step opacity and complexity considerations[J]. IEEE Transactions on Automatic Control, 2012, 57(5): 1265-1269.

LEFEBVRE D, HADJICOSTIS C N. Exposure and revelation times as a measure of opacity in timed stochastic discrete event systems[J]. IEEE Transactions on Automatic Control, 2020, 66(12): 5802-5815.

YIN X, LI Z, WANG W, et al , Infinite-step opacity and k-step opacity of stochastic discrete event systems[J ] . Automatica, 2019, 99: 266-274.

QI G Z, LIU F C, CUI H G. Opacity verification in stochastic discrete event systems using two-way observers[J]. Journal of Guangdong University of Technology, 2023, 40(3): 32-37.

APARICIO J, LVAREZ F, LVARO H, et al . A survey on acoustic positioning systems for location-based services[J ] . IEEE Transactions on Instrumentation and Measurement, 2022, 71: 850533.

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