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Diagnosis of Pushdown Systems

Christophe Morvan 1 Sophie Pinchinat 2 
2 S4 - System synthesis and supervision, scenarios
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
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.
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Submitted on : Friday, November 7, 2008 - 2:46:48 PM
Last modification on : Friday, February 4, 2022 - 3:25:36 AM
Long-term archiving on: : Monday, June 7, 2010 - 8:32:59 PM


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  • HAL Id : inria-00337614, version 1


Christophe Morvan, Sophie Pinchinat. Diagnosis of Pushdown Systems. [Research Report] PI 1904, 2008, pp.19. ⟨inria-00337614⟩



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