2019
DOI: 10.1016/j.isatra.2019.01.023
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On-line verification of initial-state opacity by Petri nets and integer linear programming

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Cited by 22 publications
(9 citation statements)
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“…For state (5Y, {4Y, 5Y }, {0N, 1N, 2Y, 3Y, 4Y, 5Y }), when event a occurs, it reaches (7Y, {6Y, 7Y, 8N, 9N, 9Y }, {7Y }), where since a ∈ Σ o but 7Y / ∈ Xr , the third component is updated according to the second case of Equation ( 4 Theorem 2 Let Obs( G) be the DIRM-observer for system G. Then system G is current-state opaque w.r.t. X S and X r if and only if ∀x obs ∈ X obs : X 3 (x obs ) XS (13) We illustrate Theorem 2 by the following example. 3), where for x = (7Y, {6Y, 7Y, 8Y, 9Y, 9N }, {7Y }), we have X 3 (x) = {7Y } ⊆ XS .…”
Section: Inductionmentioning
confidence: 99%
“…For state (5Y, {4Y, 5Y }, {0N, 1N, 2Y, 3Y, 4Y, 5Y }), when event a occurs, it reaches (7Y, {6Y, 7Y, 8N, 9N, 9Y }, {7Y }), where since a ∈ Σ o but 7Y / ∈ Xr , the third component is updated according to the second case of Equation ( 4 Theorem 2 Let Obs( G) be the DIRM-observer for system G. Then system G is current-state opaque w.r.t. X S and X r if and only if ∀x obs ∈ X obs : X 3 (x obs ) XS (13) We illustrate Theorem 2 by the following example. 3), where for x = (7Y, {6Y, 7Y, 8Y, 9Y, 9N }, {7Y }), we have X 3 (x) = {7Y } ⊆ XS .…”
Section: Inductionmentioning
confidence: 99%
“…Consequently, the authors resort to integer linear programming (ILP) to solve this problem. In the same context, online verification algorithms for current 38 and initial 39 state opacity have been proposed by Cong et al in LPNs by assuming the acyclicity of the observable and unobservable subnets. These algorithms detect the occurrence of events and decide whether the transition (event) sequence observed so far is opaque or not.…”
Section: Introductionmentioning
confidence: 99%
“…This decision is based on solving a group of ILPs. The works in 38 , 39 are restricted to secret markings defined by generalized mutual exclusion constraints (GMECs) 40 .…”
Section: Introductionmentioning
confidence: 99%
“…Petri nets [3], as a major mathematical model, have been applied to many problems in discrete event systems [4]- [10], such as modeling and analysis [11], [52], control [12]- [17], opacity verification and enforcement [18], [19], scheduling [20]- [28], [50], [51], performance evaluation [29], [30], [53], fault identification and diagnosis [32], [33], [61], [62], validation of various properties [18], [19], [54], and deadlock analysis and control [31], [32], [34], [35], [45]- [48].…”
Section: Introductionmentioning
confidence: 99%