Diagnosis and opacity problems for infinite state systems modeled by recursive tile systems

Abstract

The analysis of discrete event systems under partial observation is an important topic, with major applications such as the detection of information flow and the diagnosis of faulty behaviors. These questions have, mostly, not been addressed for classical models of recursive systems, such as pushdown systems and recursive state machines. In this paper, we consider recursive tile systems, which are recursive infinite systems generated by a finite collection of finite tiles, a simplified variant of deterministic graph grammars (slightly more general than pushdown systems). Since these systems are infinite-state in general powerset constructions for monitoring do not always apply. We exhibit computable conditions on recursive tile systems and present non-trivial constructions that yield effective computation of the monitors. We apply these results to the classic problems of state-based opacity and diagnosability (off-line verification of opacity and diagnosability, and also runtime monitoring of these properties). For a decidable subclass of recursive tile systems, we also establish the decidability of the problems of state-based opacity and diagnosability.

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

“…There are recent works addressing extensions to infinite-state. CSO and diagnosability verification are investigated for infinite-state DES modeled by pushdown automata in Kobayashi & Hiraishi (2013) (therein called pushdown systems), as well as in Chédor et al (2014) and Chédor (2014), in the more general setting of recursive tile systems.…”

“…Some instances of opacity problem can be formulated as diagnosis ones (e.g., resolution of ISO from Hadjicostis (2012)). As a result, several opacity-related works try to bridge with the huge amount of work done in the diagnosis community; e.g., Dubreil et al (2009); Dubreil (2010); Kobayashi & Hiraishi (2013); Chédor et al (2014).…”

“…Note that LBO, ISO, CSO, and IFO-referred to as general opacity problems -have been proven to be reducible into one another in polynomial time (Wu & Lafortune (2013), Chédor et al (2014)). Therefore, these problems have same decidability and complexity (since their complexity is, at least, polynomial).…”

Opacity of Discrete Event Systems: models, validation and quantification

“…There are recent work addressing extensions to infinitestate DES. CSO and diagnosability verification are investigated for infinite-state DES modeled by pushdown automata in Kobayashi and Hiraishi (2013) (therein called pushdown systems), as well as in Chédor et al (2014), in the more general setting of recursive tile systems.…”

“…This sections synthesizes decidability and complexity results demonstrated in the literature. Note that LBO, ISO and CSO -referred to as general opacity problems -have been proven to be reducible into one another in polynomial time (Wu and Lafortune (2013), Chédor et al (2014)). Therefore, these problems have same decidability and complexity (since their own complexity is at least polynomial).…”