Diagnosability Verification with Parallel LTL-X Model Checking Based on Petri Net Unfoldings Agnes Madalinski 1, and Victor Khomenko 2 1 Faculty of Engineering Science, University Austral de Chile 2 School of Computing Science, Newcastle University, UK

2 Outline Concept of fault diagnosis and diagnosability Diagnosability verification with LTL-X model checking Experimental result Conclusions and future work

3 Concept of fault diagnosis system diagnosis observations faults detection, localisation and identification of faults diagnosis: task of explaining abnormal behaviours of a system given observations about its behaviour diagnosability: the possibility of detecting faults by monitoring the visible behaviour of the system actions (repair, reconfigure)

4 Diagnosability diagnosis observations fault occurred? o 1, o 2, o 3, o 4,o 5 A system is diagnosable if an occurrence of a fault can be detected with certainty in a bounded time. system

5 Diagnosability aaXcdacYddeaaZcc… For a system with finite state space: absence of two infinite traces having the same observable traces one having a fault and the other not having one XYZ… ccaXdYfadeaaaZee…

6 System model O = {a} U = {u, f} F = {f} labelled Petri net N = (P,T →,M 0,O,U, ℓ )‏ O set of observable transition labels U set of unobservable transition labels ℓ : T → O  U F  U set of fault transition labels

7 Fault tracking f’ fault tracking net N ft for state based LTL-X model checking

8 Verifier sync. product of two replicas of N ft on observable transitions a trace in verifier represents a pair of traces of N ft with the same projection on observable transitions

9 Expressing non-diagnosability in LTL-X diag = ◊p f 1 ∧ □p f 2 eventually p f 1 is marked (fault occures in N ft 1 ) p f 2 always stays marked (no fault in N ft 2 ) Büchi automaton accepting diag

10 Simplifying the verifier diag = ◊p f 1 ∧ □p f 2 f 2 must never fire enforced by removing the transitions f 2 and f’ 2

11 Simplifying the verifier diag = ◊p f 1 ∧ □p f 2

12 Unfolding Approach to LTL-X Model-Checking Net system is constructed as composition of verifier and the Büchi automaton accepting diag Efficient Petri net unfolding based LTL-X model checking Relies on the partial order view of concurrent computation Represents states implicitly, using an acyclic net Esparza and Heljanko (ICALP 2000, SPIN 2001) Parallel LTL-X model-checker for high level Petri nets by Schröter and Khomenko (CAV 2004), implemented in PUNF tool

13 Tools used for experiments PComp: to compute the verifier PUNF: parallel LTL-X model checker Available at:

14 Experiments: assorted benchmarks diagnosable

15 Experiments: scalable pipelines (non-diag.)

16 Experiments: scalable pipelines (diag.)

17 Experiments: parallel mode 16,777,216 upper bound on the number of states of the verifier

18 Conclusions Experimental results show that the method works quite well, especially on highly concurrent systems A good level of parallelisation has been achieved However the benchmarks are rather artificial Larger and more practical benchmarks are needed Proposed approach can be trivialy generalised to high- level Petri nets