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Ch. Morvan, S. Pinchinat. Diagnosis of Pushdown Systems. Research Report IRISA, No 1904, October 2008.

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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


Christophe Morvan http://www-igm.univ-mlv.fr/~cmorvan/

BibTex Reference

   Author = {Morvan, Ch. and Pinchinat, S.},
   Title = {Diagnosis of Pushdown Systems},
   Number = {1904},
   Institution = {IRISA},
   Month = {October},
   Year = {2008}

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