Opaque superlanguages and sublanguages in discrete event systems

Abstract

Abstract-Opacity describes the inability for an external observer to know what happened in a system. Recently, opacity has been investigated in the framework of discrete event systems. In our previous paper, we define two types of opacities: strong opacity and weak opacity. Given a general observation mapping, a language is strongly opaque if all strings in the language are confused with some strings in another language and it is weakly opaque if some strings in the language are confused with some strings in another language. In this paper, we investigate properties of opacities. We show that opacities are closed under union, but may not be closed under intersection. Based on these properties, we discuss how to modify languages to satisfy the strong opacity, weak opacity, and no opacity by investigating the sublanguages and superlanguages that are strongly opaque, weakly opaque, and not opaque respectively. We find the largest sublanguages and smallest superlanguages. Examples are given to illustrate results.

Notions of Centralized and Decentralized Opacity in Linear Systems

“…A subsequent paper [26] defined opacity for DESs in a decentralized framework with multiple adversaries, each carrying out its own observation of the system. The authors of [27] characterized languagebased notions of opacity under unions and intersections. They demonstrated the existence of supremal and minimal opaque sublanguages and superlanguages.…”

Overview of discrete event systems opacity: Models, validation, and quantification

“…As a consequence, we can further define easily the property of no opacity. Lin (2009) that LBO properties are closed under union, but may not be closed under intersection. They further discuss how to modify languages to satisfy the strong, weak, and no opacity by investigating sublanguages and superlanguages.…”

“…In a nutshell, supervisory control resumes to find the supremal sublanguage that ensures opacity. In Ben-Kalefa & Lin (2009), the authors further investigate language composition and show that opacity properties (with secrets being languages) are closed under union, but may not be closed under intersection. They also demonstrate the following results: (i) the supremal strongly opaque sublanguage exists and is unique;…”

A survey of the opacity of discrete event systems

“…The language-based opacity is divided into strong opacity and weak opacity according to the coincidence degree between secret language and non-secret language [8] . The researchers make the system meet the characteristics of strong opacity,weak opacity and complete transparency by modifying the language set [9] . Not only for classic DES,the more complex opacity properties of probability DES [10][11][12] random DES [13][14][15] have been studied in depth.At the same time,the more complex modular system [16,17] has also been studied.These more complex systems are more suitable for practical industrial production applications.For checking whether the system has opacity properties, the verification method is generally adopted [18][19][20] .…”