Diagnosability of Pushdown Systems

Abstract

Diagnosis problems of discrete-event systems consist in detecting unobservable defects during system execution. For finite-state systems, the theory is well understood and a number of effective solutions have been developed. For infinite-state systems, however, there are only few results, mostly identifying classes where the problem is undecidable.We consider higher-order pushdown systems and investigate two basic variants of diagnosis problems: the diagnosability, which consists in deciding whether defects can be detected within a finite delay, and the bounded-latency problem, which consists in determining a bound for the delay of detecting defects.We establish that the diagnosability problem is decidable for arbitrary sub-classes of higher-order visibly pushdown systems provided unobservable events leave the stacks unchanged. For this case, we present an effective algorithm. Otherwise, we show that diagnosability becomes undecidable already for first-order visibly pushdown automata. Furthermore, we establish that the bounded-latency problem for higher-order pushdown systems is as hard as deciding finiteness of a higher-order pushdown language. This is in contrast with the case of finite-state systems where the problem reduces to diagnosability.Key-words: Pushdown systems, Visibly pushdown systems, Partial observation, Diagnosis. Diagnostic des Systèmesà PilesRésumé : Les problèmes de diagnostic des systèmesàévénements discrets examinent la détection de défauts inobservables au cours de l'exécution du système. Pour les systèmesà nombre d'états fini, la théorie est déjà bien maîtrisée, et de nombreuses solutions effectives ontété développées. En revanche, le cas des systèmesà nombre d'états infini n'a fait l'objet que de peu d'études, exhibant le plus souvent des problèmes indécidables. Nous considérons les systèmesà piles d'ordre supérieur etétudions deux problèmeś elémentaires de diagnostic : la diagnosticabilité, problème pour lequel il s'agit de décider si les défauts seront détectés en un temps fini, et le problème de la latence bornée, pour lequel on souhaite déterminer si le décalage temporel entre l'occurrence d'un défaut et sa détection est borné.Nousétablissons que la diagnosticabilité est décidable pour toute sous-classe de systèmes a piles d'ordre supérieur dès lors que que toutévénement inobservable ne modifie l'état des piles. Dans ce cas, nous présentons des algorithmes. Autrement, nous montrons que la diagnosticabilité est indécidable pour la sous-classe des systèmes dits "visibly pushdown", un classique de la littérature. En outre, nousétablissons que le problème de la latence bornée pour les systèmesà piles d'ordre supérieur est au moins aussi difficile que celui de décider la finitude des langagesà piles d'ordre supérieur. Ce dernier résultat est en opposition avec le cas des systèmesà nombre d'états fini pour lesquels le problème de la latence bornée se réduità celui de diagnosticabilité.

Active Diagnosis for Probabilistic Systems

“…Diagnosis and diagnosability checking have been extended to numerous models (Petri nets [CGLS09], pushdown systems [MP09], etc.) and settings (centralized, decentralized, distributed), and have had an impact on important application areas, e.g.…”

Analysis of partially observed recursive tile systems

“…We identify decidable hypothesis under which the opacity and the diagnosis problems can be solved. The present work strictly extends the results of Morvan and Pinchinat (2009), and relies on a new approach with non-trivial constructions and transformation on graph grammars. In this presentation, we define RTS as objects generated by a finite set of tiles, a formalism equivalent to deterministic graph grammars introduced in Chédor et al (2012).…”

“…This result is a consequence of Morvan and Pinchinat (2009) since visibly pushdown systems are a strict subclass of weighted RTS. However, we have a result similar to Theorem 1.…”

“…With the same objective, Hélouet et al (2006) consider a distributed observation of a distributed system modeled by a High Level Message Sequence Chart. Recently, Morvan and Pinchinat (2009) consider pushdown systems and show that the diagnosability property is decidable for a subclass of visibly pushdown systems. As exemplified in the literature, opacity and diagnosis problems can be solved by using common techniques: the ability to compute an �-closure (a projection), to perform a standard determinization preserving state properties, to compute a self-product or simulate it as a game, to detect infinite executions, and to support reachability analysis.…”

Diagnosability degree of stochastic discrete event systems

“…Rather than diagnosis itself, numerous contributions have considered the diagnosability property, which means that the presence of a fault can be detected in bounded time after its occurrence. Diagnosability has been studied for numerous models (automata [1], [3], Petri nets [5], concurrent systems [6], [7], visibly push-down automata [8]...). It has been extended to stochastic systems [9]- [15], and to distributed or decentralized settings.…”