Diagnosis of Large Software Systems Based on Colored Petri Nets

Transcription

1 Diagnosis of Large Software Systems Based on Colored Petri Nets Supervised by Tarek Melliti 2 and Philippe Dague 1 Yingmin Li 1 1 LRI IASI, Univ. Paris-Sud, CNRS/INRIA Saclay, France 2 IBISC, Univ. d Evry Val d Essonne, CNRS, France December 9, / 101

2 Context: basic Web services Web service: Technology allowing applications to dialogue remotely via Internet independently of the platforms and the languages they rest on. Cheaper and simpler for connection and integration. 2 / 101

3 Context: composite Web services A travel agency example An orchestrated Web service consists of a travel agency, an airline search engine, and a bank billing system On 09/07/2010, a client, reserved a round trip Paris-Rome, 07/11/ /12/ /07/ /12/2010 Paris-Rome The cheapest flight should be around 200 euros. I have 500 euros in my account 3 / 101

4 Context: diagnosis problems of Web services A travel agency example Reservation failed because of no enough credit? Client was confused and asked why the tickets were so expensive No enough credit 09/07/ /12/2010 Paris-Rome The cheapest flight should be around 200 euros. I have 500 euros in my account Alarm Fault 4 / 101

5 An abstract view Large software systems Consist of several components located on different sites Dysfunctions are generated and transformed among the components through data (signals, interface data, etc) A communicating components system Fault Component1 Component2 Observation Completely ordered: O1, O2,..., On Component3 Alarm Partially ordered: O1, O3 O2, O4 Non-ordered: {O1, O2,..., On} On Diagnosis To detect and explain the possible fault(s) 5 / 101

6 A possible solution: model based diagnosis A communicating components system diagnosis Component1 Partially ordered obs O1, O3 Abstract system model Fault Component2 Diagnoser O2, O4 Partially ordered obs Component3 Alarm Partially ordered obs O5, O6 Diagnosis To detect and explain the possible data, control or event fault(s) might come from other components 6 / 101

7 A possible solution: model based diagnosis To model the faulty events as unobservable events Component1 Partially ordered obs O1, O3 Abstract system model Fault Component2 Diagnoser O2, O4 Partially ordered obs Component3 Alarm Partially ordered obs O5, O6 Diagnosis To detect and explain the possible data, control or event fault(s) might come from other components 7 / 101

8 Existing works DES models Discrete event system (DES) models: Petri net (Petri [1973]), automata (Arto and N. [1969]), process algebra (van Glabbeek [1987]), etc. Most of them focus on the state evolution driven by the discrete events Faults are modeled as unobservable events (Sampath et al. [1995]) while faulty data is usually not modeled 8 / 101

9 Existing works: diagnoser (Sampath et al. [1995, 1996]) Transform the discrete event model of the system to be diagnosed into a finite state automaton which has only observable events; the historical faulty events are recorded in states. Example f1 t2 t1 N t2 t1 f2 f1 N t3 observations: t 2 t 3 Diagnosis={f 2 } t3 f2 system diagnoser 9 / 101

10 Existing works: PN unfolding (Benveniste et al. [2003]) Fully describes the concurrent behaviors in a single branching structure, represents all the possible computation steps and their mutual dependencies, as well as all reachable states. Example system observations unfolding diagnoser 10 / 101

11 Existing works: PN backward reasoning (Anglano and Portinale [1994]; Cardoso et al. [1995]; Jiroveanu [2006]; Srinivasan and Jafari [1994]) Starts from the final states which represents a symptom and calculates backwardly according to the backward searching rules to detect all the traces that cover it. Example t 1 system observation diagnosis 11 / 101

12 Assumptions Targets Locally correct and tested software system with interacting components in a stable network environment, but faulty activities, faulty data and controls (from user, database, interface, etc) that transmitted between the components Symptoms Exception(s) thrown on one or more components during the execution Method: model based diagnosis Component2 Fault Fault O2, O4 Partially ordered obs Component1 Partially ordered obs O1, O3 Component3 Partially ordered obs O5, O6 Alarm? Abstract system model??? 12 / 101

13 Challenges Existing works focus on state evolution diagnose by trajectories reconstruction We need an abstract model to represent the correct and fault of data and controls in a unique way to represent the correct and fault behaviors of the activities to represent the concurrency and partially ordered observations allows to handle the loops in an elegant way to avoid unfolding the trajectories to diagnose the orchestrated software systems Our choice Colored Petri net 13 / 101

14 Outline 1 Introduction Context: Web service diagnosis problem Model-based diagnosis for Web services Assumptions 2 Abstract model: CPN CPN definition Partially ordered observation 3 Diagnosis CPN as a fault model Diagnosis algorithm 4 Application Architecture of BPEL Monitoring and Diagnosis Decentralized diagnosis architecture Example: travel agency diagnosis problem 5 Conclusions & perspectives Contributions Perspectives 14 / 101

15 CPN has same structure as PN Example p 1 2 t 3 p 2 Definition (Petri net) N= P, T, Pre, Post P: a set of labeled places T : a set of labeled transitions Pre : P T N, a backward matrix of consumed token number Post : P T N, a forward matrix of produced token number Example (Incidence matrix C=Post-Pre) C t p 1-2 p 2 3 = Post t p 1 p Pre t p 1 2 p 2 Example (State equation) M = M 0 + C T p p / 101

16 CPN has same structure as PN Example p 1 2 t 3 p 2 Definition (Petri net) N= P, T, Pre, Post P: a set of labeled places T : a set of labeled transitions Pre : P T N, a backward matrix of consumed token number Post : P T N, a forward matrix of produced token number Example (Incidence matrix C=Post-Pre) C t p 1-2 p 2 3 = Post t p 1 p Pre t p 1 2 p 2 Example (State equation) M = M 0 + C T p p / 101

17 CPN has same structure as PN Example p t p 2 Definition (Petri net) N= P, T, Pre, Post P: a set of labeled places T : a set of labeled transitions Pre : P T N, a backward matrix of consumed token number Post : P T N, a forward matrix of produced token number Example (Incidence matrix C=Post-Pre) C t p 1-2 p 2 3 = Post t p 1 p Pre t p 1 2 p 2 Example (State equation) M = M 0 + C T p p / 101

18 CPN definition: Structure & dynamic (Li et al. [2009a]) Example p 1 : Π 1 F : Γ 1 Ψ(Π 1 ) t : Γ 1 F : Γ 1 Ψ(Π 2 ) p 2 : Π 2 PN to CPN Places are typed (p 1 : Π 1 ) Transition are typed (t : Γ 1 ) Markings are multi-sets of place types (m(p 1 ) = n i e i, n i 0, e i Π 1 ) i Π 1 Weights of an edges are multi-set expressions (Pre(p 1, t) : Γ 1 Ψ(Π 1 )) 18 / 101

19 CPN definition: Structure & dynamic (Li et al. [2009a]) Example p 1 : Π 1 F : Γ 1 Ψ(Π 1 ) t : Γ 1 F : Γ 1 Ψ(Π 2 ) p 2 : Π 2 PN to CPN Places are typed (p 1 : Π 1 ) Transition are typed (t : Γ 1 ) Markings are multi-sets of place types (m(p 1 ) = n i e i, n i 0, e i Π 1 ) i Π 1 Weights of an edges are multi-set expressions (Pre(p 1, t) : Γ 1 Ψ(Π 1 )) Example (Binding β) β 1m1 : {x = a} or β 2m1 : {x = b} 1 a+ 2 b p 1 : Π 1 = {a, b} Pre(t, p 1 ) = {(m 1 : 1 b + 1 x),(m 2 : 1 a)} t : Γ 1 = {m 1, m 2 } Post(t, p 2 ) = {(m 1 : 2 x), (m 2 : 2 c)} Mode firing rule: M[t m β M M = M + C(., t)(m 1 ) β with β : x = a Marking: M is reachable from M under β and m can be extended to sequence firing 1 c p 2 : Π 2 = {a, b, c} 19 / 101

20 CPN definition: Structure & dynamic (Li et al. [2009a]) Example p 1 : Π 1 F : Γ 1 Ψ(Π 1 ) t : Γ 1 F : Γ 1 Ψ(Π 2 ) p 2 : Π 2 PN to CPN Places are typed (p 1 : Π 1 ) Transition are typed (t : Γ 1 ) Markings are multi-sets of place types (m(p 1 ) = n i e i, n i 0, e i Π 1 ) i Π 1 Weights of an edges are multi-set expressions (Pre(p 1, t) : Γ 1 Ψ(Π 1 )) Example (Binding β) β 1m1 : {x = a} or β 2m1 : {x = b} 1 b p 1 : Π 1 = {a, b} Pre(t, p 1 ) = {(m 1 : 1 b + 1 x),(m 2 : 1 a)} t : Γ 1 = {m 1, m 2 } Post(t, p 2 ) = {(m 1 : 2 x), (m 2 : 2 c)} Mode firing rule: M[t m β M M = M + C(., t)(m 1 ) β with β : x = a Marking: M is reachable from M under β and m can be extended to sequence firing 1 c p 2 : Π 2 = {a, b, c} 20 / 101

21 CPN definition: Structure & dynamic (Li et al. [2009a]) Example p 1 : Π 1 F : Γ 1 Ψ(Π 1 ) t : Γ 1 F : Γ 1 Ψ(Π 2 ) p 2 : Π 2 PN to CPN Places are typed (p 1 : Π 1 ) Transition are typed (t : Γ 1 ) Markings are multi-sets of place types (m(p 1 ) = n i e i, n i 0, e i Π 1 ) i Π 1 Weights of an edges are multi-set expressions (Pre(p 1, t) : Γ 1 Ψ(Π 1 )) Example (Binding β) β 1m1 : {x = a} or β 2m1 : {x = b} 1 b p 1 : Π 1 = {a, b} Pre(t, p 1 ) = {(m 1 : 1 b + 1 x),(m 2 : 1 a)} t : Γ 1 = {m 1, m 2 } Post(t, p 2 ) = {(m 1 : 2 x), (m 2 : 2 c)} Mode firing rule: M[t m β M M = M + C(., t)(m 1 ) β with β : x = a Marking: M is reachable from M under β and m can be extended to sequence firing 1 c + 2 a p 2 : Π 2 = {a, b, c} 21 / 101

22 CPN definition: Dynamic Definition (Characteristic Vector) Sequence of modes: δ Mod Characteristic vector of δ: δ : Mod N Transition characteristic vector δ T : T N Example δ = t 1.m 1 t 2.m 3 t 1.m 2 t 1.m 1 t 1.m 2 δ (m1 ) = 2 δ T (t 1 ) = 4 State equation Given S= N, M a CPN-S and modes sequence, δ Mod with M[δ then the reached marking M after the firing of δ is : M = M + C δ 22 / 101

23 CPN definition: example (1/2) Dining philosophers (of size four) No blocking version (taking both forks concurrently) Forks are identified by the serial number 1-4 One of them (num 4) is well-organized: to take the forks, and before eat, he/she checks the id of the forks Three of them (num 1, 2 and 3) are Unorganized: don t verify the forks id and might exchange forks in hands before restore them. 23 / 101

24 CPN definition: example (2/2) Notations p i : the forks on the table t i and r i : philosopher i takes and released the fork p ii : the fork in the right hand of philosopher i p ji : the fork in the left hand of philosopher i Normal:χp 11 Normal:χp r 21 Exchange:χp 1 21 Exchange:χp 11 χ p11 χ p21 Normal:χp 14 p 14 χp χ 1 p14 r 4 t 4 χ p44 χp 4 p 11 p 21 χp 1 χp t 2 1 χ p1 χ p2 p 1 1 p 2 2 χ p1 χ p2 χ p4 χ p3 Normal:χp 22 Exchange:χp 32 p 22 χp 2 χ p22 t 2 r 2 χp 3 χ p32 p 44 p 4 4 χ p4 χ p3 p 3 3 p 32 Normal:χp 44 χp 4 t 3 χp 3 Normal:χp 32 Exchange:χp 22 p 43 p 33 χ p43 χ p33 Normal:χp 43 Exchange:χp 33 r 3 Normal:χp33 Exchange:χp / 101

25 CPN definition: example (2/2) Notations Normal:χp 11 Normal:χp r 21 Exchange:χp 1 21 Exchange:χp 11 p i : the forks on the table χ p11 χ p21 p 11 p 21 t i and r i : philosopher i takes and released the fork p ii : the fork in the right hand of philosopher i Normal:χp 14 p 14 χp χ 1 p14 χp 1 χp t 2 1 χ p1 χ p2 p 1 p 2 χ p1 χ p2 Normal:χp 22 Exchange:χp 32 p 22 χp 2 χ p22 p ji : the fork in the left hand of philosopher i r 4 χ p44 t 4 χp 4 t 2 r 2 χp 3 χ p32 χ p4 χ p3 p 44 p 4 χ p4 χ p3 p 3 p 32 Normal:χp 44 χp 4 t 3 χp 3 Normal:χp 32 Exchange:χp 22 p 43 p 33 χ p43 χ p33 Normal:χp 43 Exchange:χp 33 r 3 Normal:χp33 Exchange:χp / 101

26 CPN definition: example (2/2) Notations Normal:χp 11 Normal:χp r 21 Exchange:χp 1 21 Exchange:χp 11 p i : the forks on the table χ p11 χ p21 p 11 p 21 t i and r i : philosopher i takes and released the fork p ii : the fork in the right hand of philosopher i Normal:χp 14 p 14 χ p14 1 χp 1 χp 1 χp t 2 1 χ p1 χ p2 p 1 p 2 χ p1 χ p2 Normal:χp 22 Exchange:χp 32 p 22 χp 2 2 χ p22 p ji : the fork in the left hand of philosopher i r 4 χ p44 t 4 χp 4 t 2 r 2 χp 3 χ p32 χ p4 χ p3 p 44 4 p 4 χ p4 χ p3 p 3 p 32 3 Normal:χp 44 χp 4 t 3 χp 3 Normal:χp 32 Exchange:χp 22 p 43 p 33 χ p43 χ p33 Normal:χp 43 Exchange:χp 33 r 3 Normal:χp33 Exchange:χp / 101

27 CPN definition: example (2/2) Notations Normal:χp 11 Normal:χp r 21 Exchange:χp 1 21 Exchange:χp 11 p i : the forks on the table χ p11 χ p21 p 11 p 21 t i and r i : philosopher i takes and released the fork p ii : the fork in the right hand of philosopher i Normal:χp 14 p 14 χp χ 1 p14 χp 1 χp t 2 1 χ p1 χ p2 p 1 p 2 χ p1 χ p2 Normal:χp 22 Exchange:χp 32 p 22 χp 2 χ p22 p ji : the fork in the left hand of philosopher i r 4 χ p44 t 4 χp 4 t 2 r 2 χp 3 χ p32 χ p4 χ p3 p 44 p 4 χ p4 χ p3 p 3 p 32 Normal:χp 44 χp 4 t 3 χp 3 Normal:χp 32 Exchange:χp 22 p 43 p 33 χ p43 χ p33 Normal:χp 43 Exchange:χp 33 r 3 Normal:χp33 Exchange:χp / 101

28 CPN definition: example (2/2) Notations Normal:χp 11 Normal:χp r 21 Exchange:χp 1 21 Exchange:χp 11 p i : the forks on the table χ p11 χ p21 p 11 p 21 t i and r i : philosopher i takes and released the fork p ii : the fork in the right hand of philosopher i Normal:χp 14 p 14 χp χ 1 p14 χp 1 χp t 2 1 χ p1 χ p2 p 1 1 p 2 3 χ p1 χ p2 Normal:χp 22 Exchange:χp 32 p 22 χp 2 χ p22 p ji : the fork in the left hand of philosopher i r 4 χ p44 t 4 χp 4 t 2 r 2 χp 3 χ p32 χ p4 χ p3 p 44 p 4 4 χ p4 χ p3 p 3 2 p 32 Normal:χp 44 χp 4 t 3 χp 3 Normal:χp 32 Exchange:χp 22 p 43 p 33 χ p43 χ p33 Normal:χp 43 Exchange:χp 33 r 3 Normal:χp33 Exchange:χp / 101

29 CPN definition: example (2/2) Notations Normal:χp 11 Normal:χp r 21 Exchange:χp 1 21 Exchange:χp 11 p i : the forks on the table χ p11 χ p21 p 11 p 21 t i and r i : philosopher i takes and released the fork p ii : the fork in the right hand of philosopher i Normal:χp 14 p 14 χp χ 1 p14 χp 1 χp t 2 1 χ p1 χ p2 p 1 p 2 χ p1 χ p2 Normal:χp 22 Exchange:χp 32 p 22 χp 2 χ p22 p ji : the fork in the left hand of philosopher i r 4 χ p44 t 4 χp 4 t 2 r 2 χp 3 χ p32 χ p4 χ p3 p 44 p 4 χ p4 χ p3 p 3 p 32 Normal:χp 44 χp 4 t 3 χp 3 Normal:χp 32 Exchange:χp 22 p 43 p 33 χ p43 χ p33 Normal:χp 43 Exchange:χp 33 r 3 Normal:χp33 Exchange:χp / 101

30 CPN definition: example (2/2) Notations Normal:χp 11 Normal:χp r 21 Exchange:χp 1 21 Exchange:χp 11 p i : the forks on the table χ p11 χ p21 p p 21 t i and r i : philosopher i takes and released the fork p ii : the fork in the right hand of philosopher i Normal:χp 14 p 14 χp χ 1 p14 χp 1 χp t 2 1 χ p1 χ p2 p 1 p 2 χ p1 χ p2 Normal:χp 22 Exchange:χp 32 p 22 χp 2 χ p22 p ji : the fork in the left hand of philosopher i r 4 χ p44 t 4 χp 4 t 2 r 2 χp 3 χ p32 χ p4 χ p3 p 44 p 4 χ p4 χ p3 p 3 p 32 Normal:χp 44 χp 4 t 3 χp 3 Normal:χp 32 Exchange:χp 22 p p 33 χ p43 χ p33 Normal:χp 43 Exchange:χp 33 r 3 Normal:χp33 Exchange:χp / 101

31 CPN definition: example (2/2) Notations Normal:χp 11 Normal:χp r 21 Exchange:χp 1 21 Exchange:χp 11 p i : the forks on the table χ p11 χ p21 p 11 p 21 t i and r i : philosopher i takes and released the fork p ii : the fork in the right hand of philosopher i Normal:χp 14 p 14 χp χ 1 p14 χp 1 χp t 2 1 χ p1 χ p2 p 1 p 2 χ p1 χ p2 Normal:χp 22 Exchange:χp 32 p 22 χp 2 χ p22 p ji : the fork in the left hand of philosopher i r 4 χ p44 t 4 χp 4 t 2 r 2 χp 3 χ p32 χ p4 χ p3 p 44 p 4 χ p4 χ p3 p 3 p 32 Normal:χp 44 χp 4 t 3 χp 3 Normal:χp 32 Exchange:χp 22 p 43 p 33 χ p43 χ p33 Normal:χp 43 Exchange:χp 33 r 3 Normal:χp33 Exchange:χp / 101

32 CPN definition: example (2/2) Notations Normal:χp 11 Normal:χp r 21 Exchange:χp 1 21 Exchange:χp 11 p i : the forks on the table χ p11 χ p21 p 11 p 21 t i and r i : philosopher i takes and released the fork p ii : the fork in the right hand of philosopher i Normal:χp 14 p 14 χp χ 1 p14 χp 1 χp t 2 1 χ p1 χ p2 p 1 3 p 2 1 χ p1 χ p2 Normal:χp 22 Exchange:χp 32 p 22 χp 2 χ p22 p ji : the fork in the left hand of philosopher i r 4 χ p44 t 4 χp 4 t 2 r 2 χp 3 χ p32 χ p4 χ p3 p 44 p 4 2 χ p4 χ p3 p 3 4 p 32 Normal:χp 44 χp 4 t 3 χp 3 Normal:χp 32 Exchange:χp 22 p 43 p 33 χ p43 χ p33 Normal:χp 43 Exchange:χp 33 r 3 Normal:χp33 Exchange:χp / 101

33 CPN definition: example (2/2) Notations Normal:χp 11 Normal:χp r 21 Exchange:χp 1 21 Exchange:χp 11 p i : the forks on the table χ p11 χ p21 p 11 p 21 t i and r i : philosopher i takes and released the fork p ii : the fork in the right hand of philosopher i Normal:χp 14 p 14 χp χ 1 p14 χp 1 χp t 2 1 χ p1 χ p2 p 1 p 2 χ p1 χ p2 Normal:χp 22 Exchange:χp 32 p 22 χp 2 χ p22 p ji : the fork in the left hand of philosopher i r 4 χ p44 t 4 χp 4 t 2 r 2 χp 3 χ p32 χ p4 χ p3 p 44 p 4 χ p4 χ p3 p 3 p 32 Normal:χp 44 χp 4 t 3 χp 3 Normal:χp 32 Exchange:χp 22 p 43 p 33 χ p43 χ p33 Normal:χp 43 Exchange:χp 33 r 3 Normal:χp33 Exchange:χp / 101

34 CPN definition: example (2/2) Notations Normal:χp 11 Normal:χp r 21 Exchange:χp 1 21 Exchange:χp 11 p i : the forks on the table χ p11 χ p21 p p 21 t i and r i : philosopher i takes and released the fork p ii : the fork in the right hand of philosopher i Normal:χp 14 p 14 χp χ 1 p14 χp 1 χp t 2 1 χ p1 χ p2 p 1 p 2 χ p1 χ p2 Normal:χp 22 Exchange:χp 32 p 22 χp 2 χ p22 p ji : the fork in the left hand of philosopher i r 4 χ p44 t 4 χp 4 t 2 r 2 χp 3 χ p32 χ p4 χ p3 p 44 p 4 χ p4 χ p3 p 3 p 32 Normal:χp 44 χp 4 t 3 χp 3 Normal:χp 32 Exchange:χp 22 p p 33 χ p43 χ p33 Normal:χp 43 Exchange:χp 33 r 3 Normal:χp33 Exchange:χp / 101

35 CPN definition: example (2/2) Notations Normal:χp 11 Normal:χp r 21 Exchange:χp 1 21 Exchange:χp 11 p i : the forks on the table χ p11 χ p21 p 11 p 21 t i and r i : philosopher i takes and released the fork p ii : the fork in the right hand of philosopher i Normal:χp 14 p 14 χp χ 1 p14 χp 1 χp t 2 1 χ p1 χ p2 p 1 p 2 χ p1 χ p2 Normal:χp 22 Exchange:χp 32 p 22 χp 2 χ p22 p ji : the fork in the left hand of philosopher i r 4 χ p44 t 4 χp 4 t 2 r 2 χp 3 χ p32 χ p4 χ p3 p 44 p 4 χ p4 χ p3 p 3 p 32 Normal:χp 44 χp 4 t 3 χp 3 Normal:χp 32 Exchange:χp 22 p 43 p 33 χ p43 χ p33 Normal:χp 43 Exchange:χp 33 r 3 Normal:χp33 Exchange:χp / 101

36 CPN definition: example (2/2) Notations Normal:χp 11 Normal:χp r 21 Exchange:χp 1 21 Exchange:χp 11 p i : the forks on the table χ p11 χ p21 p 11 p 21 t i and r i : philosopher i takes and released the fork p ii : the fork in the right hand of philosopher i Normal:χp 14 p 14 χp χ 1 p14 χp 1 χp t 2 1 χ p1 χ p2 p 1 3 p 2 1 χ p1 χ p2 Normal:χp 22 Exchange:χp 32 p 22 χp 2 χ p22 p ji : the fork in the left hand of philosopher i r 4 χ p44 t 4 χp 4 t 2 r 2 χp 3 χ p32 χ p4 χ p3 p 44 p 4 4 χ p4 χ p3 p 3 2 p 32 Normal:χp 44 χp 4 t 3 χp 3 Normal:χp 32 Exchange:χp 22 p 43 p 33 χ p43 χ p33 Normal:χp 43 Exchange:χp 33 r 3 Normal:χp33 Exchange:χp / 101

37 CPN definition: example (2/2) Notations Normal:χp 11 Normal:χp r 21 Exchange:χp 1 21 Exchange:χp 11 p i : the forks on the table χ p11 χ p21 p 11 p 21 t i and r i : philosopher i takes and released the fork p ii : the fork in the right hand of philosopher i Normal:χp 14 p 14 χp χ 1 p14 χp 1 χp t 2 1 χ p1 χ p2 p 1 p 2 χ p1 χ p2 Normal:χp 22 Exchange:χp 32 p 22 χp 2 χ p22 p ji : the fork in the left hand of philosopher i r 4 χ p44 t 4 χp 4 t 2 r 2 χp 3 χ p32 χ p4 χ p3 p 44 p 4 χ p4 χ p3 p 3 p 32 Normal:χp 44 χp 4 t 3 χp 3 Normal:χp 32 Exchange:χp 22 p 43 p 33 χ p43 χ p33 Normal:χp 43 Exchange:χp 33 r 3 Normal:χp33 Exchange:χp / 101

38 CPN definition: example (2/2) Notations Normal:χp 11 Normal:χp r 21 Exchange:χp 1 21 Exchange:χp 11 p i : the forks on the table χ p11 χ p21 p 11 p 21 t i and r i : philosopher i takes and released the fork p ii : the fork in the right hand of philosopher i Normal:χp 14 p 14 χ p14 3 χp 1 χp 1 χp t 2 1 χ p1 χ p2 p 1 p 2 χ p1 χ p2 Normal:χp 22 Exchange:χp 32 p 22 χp 2 1 χ p22 p ji : the fork in the left hand of philosopher i r 4 χ p44 t 4 χp 4 t 2 r 2 χp 3 χ p32 χ p4 χ p3 p 44 4 p 4 χ p4 χ p3 p 3 p 32 2 Normal:χp 44 χp 4 t 3 χp 3 Normal:χp 32 Exchange:χp 22 p 43 p 33 χ p43 χ p33 Normal:χp 43 Exchange:χp 33 r 3 Normal:χp33 Exchange:χp / 101

39 CPN definition: example (2/2) Notations p i : the forks on the table t i and r i : philosopher i takes and released the fork p ii : the fork in the right hand of philosopher i p ji : the fork in the left hand of philosopher i p 14 χ p14 r 4 χ p44 Normal:χp 11 Normal:χp r 21 Exchange:χp 1 21 Exchange:χp 11 χ p11 χ p21 3 p 11 p 21 χp 1 χp t 2 1 Normal:χp Normal:χp Exchange:χp 32 χ p1 χ p2 p 1 p 2 χ p1 χ p2 χp 1 t 4 χp 4 p 22 χp 2 1 χ p22 t 2 r 2 χp 3 χ p32 χ p4 χ p3 p 44 4 p 4 χ p4 χ p3 p 3 p 32 2 Normal:χp 44 χp 4 t 3 χp 3 Normal:χp 32 Exchange:χp 22 p 43 p 33 χ p43 χ p33 Normal:χp 43 Exchange:χp 33 r 3 Normal:χp33 Exchange:χp / 101

40 CPN definition: example (2/2) Notations p i : the forks on the table t i and r i : philosopher i takes and released the fork p ii : the fork in the right hand of philosopher i p ji : the fork in the left hand of philosopher i p 14 χ p14 r 4 χ p44 Normal:χp 11 Normal:χp r 21 Exchange:χp 1 21 Exchange:χp 11 χ p11 χ p21 3 p 11 p 21 χp 1 χp t 2 Normal:χp 14 1 χ p1 χ p2 p 1 p 2 2 χ p1 χ p2 χp 1 t 4 χp 4 Normal:χp 22 Exchange:χp 32 p 22 χp 2 χ p22 t 2 r 2 χp 3 χ p32 χ p4 χ p3 p 44 4 p 4 χ p4 χ p3 p 3 1 p 32 Normal:χp 44 χp 4 t 3 χp 3 Normal:χp 32 Exchange:χp 22 p 43 p 33 χ p43 χ p33 Normal:χp 43 Exchange:χp 33 r 3 Normal:χp33 Exchange:χp / 101

41 CPN definition: example (2/2) Notations p i : the forks on the table t i and r i : philosopher i takes and released the fork p ii : the fork in the right hand of philosopher i p ji : the fork in the left hand of philosopher i p 14 χ p14 r 4 χ p44 Normal:χp 11 Normal:χp r 21 Exchange:χp 1 21 Exchange:χp 11 χ p11 χ p21 3 p 11 p 21 χp 1 χp t 2 Normal:χp 14 1 χ p1 χ p2 p 1 p 2 2 χ p1 χ p2 χp 1 t 4 χp 4 Normal:χp 22 Exchange:χp 32 p 22 χp 2 χ p22 t 2 r 2 χp 3 χ p32 χ p4 χ p3 Observations p 44 4 p 4 χ p4 χ p3 p 3 1 p 32 each philosopher ate twice except philosopher 4 Normal:χp 44 χp 4 t 3 χp 3 Normal:χp 32 Exchange:χp 22 t i is fired before r i p 43 p 33 some activities were partially ordered Normal:χp 43 Exchange:χp 33 χ p43 r 3 χ p33 Normal:χp33 Exchange:χp / 101

42 Partially ordered observation Definition (Partially ordered observation (T, )) T = {t k i 1 k T (t i ) }: repeated occurred transitions (S(T) S(T)): partially ordered relation 42 / 101

43 Partially ordered observation Definition (Partially ordered observation (T, )) T = {t k i 1 k T (t i ) }: repeated occurred transitions (S(T) S(T)): partially ordered relation Example (less specific ) i = {(t (k), r (k) ),(r (k), t (k+1) )} i i i i 1 is less specific than / 101

44 Partially ordered observation Definition (Partially ordered observation (T, )) T = {t k i 1 k T (t i ) }: repeated occurred transitions (S(T) S(T)): partially ordered relation Example (less specific ) i = {(t (k), r (k) ),(r (k), t (k+1) )} i i i i 1 is less specific than 1 2 Definition (Minimal partially ordered relation MT M min ) t 1 : 2 r 1 : 2 t 2 : 2 S(T) = {t (1) 1, t(2) 1, r(1) 1, r(2) 1 r T = 2 : 2...,t t 3 (1) 4, r(1) 4 } : 2 i = {(t (k), r (k) ), i i r 3 : 2 (r (k), t (k+1) )} t 4 : 2 i i r 4 : 1 (t i, t j ) MT M min, iff δ, M[δ > M δ T = T δ t i t j M M 44 / 101

45 Adapt the CPN as a fault model An abstract fault model Define data correctness status {b, r, } Map all the transition modes into diagnostic transition modes {OK, KO} Abstract transition functionalities as data dependency functions {FW, SRC, EL} 45 / 101

46 Data dependencies in transition modes p 1 : Π 1 p 1 : Ψ D = status = {b, r, } F : Γ 1 Ψ(Π 1 ) χp : status t : Γ 1 Fault : Γ 1 {OK, KO} F : Γ 1 Ψ(Π 2 ) χp Π 1 Π 2,χ p Π 2,Π 1 Π 1 c, c status, C status, p 2 : Π 2 p 2 : status 46 / 101

47 Data dependencies in transition modes p 1 : Π 1 p 1 : Ψ D = status = {b, r, } F : Γ 1 Ψ(Π 1 ) χp : status t : Γ 1 Fault : Γ 1 {OK, KO} F : Γ 1 Ψ(Π 2 ) χp Π 1 Π 2,χ p Π 2,Π 1 Π 1 c, c status, C status, FW:status status, FW c (c) = c D = FW:Π 1 Π 2 Ψ(Π 2 ), FW(χp) = χp SRC: Ψ(Π 2 ), SRC = χp EL:(Π 1 Π 2 ) n Ψ(Π 2 ), EL(Π 1 ) = χ p D c = SRC: status, SRC c = EL :status n status, EL c (C) = c, with c = b, iff c C, c = b r, iff c C, c = r, iff c C, c = c C, c = r p 2 : Π 2 p 2 : status 47 / 101

48 Data dependencies in transition modes p 1 : Π 1 p 1 : Ψ D = status = {b, r, } F : Γ 1 Ψ(Π 1 ) χp : status t : Γ 1 Fault : Γ 1 {OK, KO} F : Γ 1 Ψ(Π 2 ) χp Π 1 Π 2,χ p Π 2,Π 1 Π 1 c, c status, C status, FW:status status, FW c (c) = c D = FW:Π 1 Π 2 Ψ(Π 2 ), FW(χp) = χp SRC: Ψ(Π 2 ), SRC = χp EL:(Π 1 Π 2 ) n Ψ(Π 2 ), EL(Π 1 ) = χ p D c = SRC: status, SRC c = EL :status n status, EL c (C) = c, with c = b, iff c C, c = b r, iff c C, c = r, iff c C, c = c C, c = r p 2 : Π 2 p 2 : status Diagnosis properties of data dependency (Ardissono et al. [2005]) EL m t c i t c j t c t m t c i t c j t c t OK b b b KO b b r OK r b r KO r b OK b KO b OK KO OK r r KO r FW m t c t c t OK/KO b b OK/KO r r OK/KO SRC m t c t OK b KO r 48 / 101

49 CPN for diagnosis: fault model Fault model: F : γ Γγ {OK, KO} F(Normal) = OK, F(Exchange) = KO Example (philosopher 1) normal:χp 11 normal:χp 21 r1 exchange:χp 21 exchange:χp 11 OK:FW(χp 11 ) KO:r r1 OK:FW(χp 21 ) KO:r χp11 χp21 χp11 χp21 p11 χp 1 χp 2 t1 p21 = p11 p21 FW(χp 1 ) FW(χp 2 ) t1 p1 1 χp1 χp2 4 p2 p1 χp1 χp2 p2 49 / 101

50 CPN for diagnosis: fault model Fault model: F : γ Γγ {OK, KO} F(Normal) = OK, F(Exchange) = KO Example (philosopher 1) normal:χp 11 exchange:r r1 normal:χp 21 exchange:r OK:FW(χp 11 ) KO:r r1 OK:FW(χp 21 ) KO:r χp11 χp21 χp11 χp21 p11 χp 1 χp 2 t1 p21 = p11 FW(χp 1 ) t1 FW(χp 2 ) p21 p1 χp1 χp2 p2 p1 χp1 χp2 p2 50 / 101

51 CPN for diagnosis: fault model Fault model: F : γ Γγ {OK, KO} F(Normal) = OK, F(Exchange) = KO Example (philosopher 1) normal:χp 11 normal:χp 21 r1 exchange:χp 21 exchange:χp 11 OK:FW(χp 11 ) KO:r r1 OK:FW(χp 21 ) KO:r χp11 χp21 χp11 χp21 p11 1 χp 1 χp 2 t1 4 p21 = p11 p21 FW(χp 1 ) t1 FW(χp 2 ) p1 χp1 χp2 p2 p1 χp1 χp2 p2 51 / 101

52 CPN for diagnosis: fault model Fault model: F : γ Γγ {OK, KO} F(Normal) = OK, F(Exchange) = KO Example (philosopher 1) normal:χp 11 normal:χp 21 r1 exchange:χp 21 exchange:χp 11 OK:FW(χp 11 ) KO:r r1 OK:FW(χp 21 ) KO:r χp11 χp21 χp11 χp21 p11 χp 1 χp 2 t1 p21 = p11 FW(χp 1 ) t1 FW(χp 2 ) p21 p1 χp1 χp2 p2 p1 χp1 χp2 p2 52 / 101

53 CPN for diagnosis: fault model Fault model: F : γ Γγ {OK, KO} F(Normal) = OK, F(Exchange) = KO Example (philosopher 1) normal:χp 11 normal:χp 21 r1 exchange:χp 21 exchange:χp 11 OK:FW(χp 11 ) KO:r r1 OK:FW(χp 21 ) KO:r χp11 χp21 χp11 χp21 p11 χp 1 χp 2 t1 p21 = p11 FW(χp 1 ) t1 FW(χp 2 ) p21 p1 4 χp1 χp2 1 p2 p1 χp1 χp2 p2 53 / 101

54 Diagnosis problem: D= M 0,(S(T ), ), ˆM (Li et al. [2009a]) Initial marking M 0 p 1 p 2 p 3 p 4 p 11 p 21 p 22 p 32 p 33 p 43 p 44 p 14,,,, 0, 0, 0, 0, 0, 0, 0, 0 Symptom ˆM p 1 p 2 p 3 p 4 p 11 p 21 p 22 p 32 p 33 p 43 p 44 p 14 0,,, 0, 0, 0, 0, 0, 0, 0, b, r (S(T ), ) t (1) 1 r (1) 1 t (2) 1 r (2) 1, t (1) 2 r (1) 2 t (2) 2 r (2) 2, t (1) 3 r (1) 3 t (2) 3 r (2) 3, t (1) r (1) t (2) / 101

55 Diagnosis problem: D= M 0,(S(T ), ), ˆM (Li et al. [2009a]) Initial marking M 0 p 1 p 2 p 3 p 4 p 11 p 21 p 22 p 32 p 33 p 43 p 44 p 14,,,, 0, 0, 0, 0, 0, 0, 0, 0 Symptom ˆM p 1 p 2 p 3 p 4 p 11 p 21 p 22 p 32 p 33 p 43 p 44 p 14 0,,, 0, 0, 0, 0, 0, 0, 0, b, r A solution for a CPN diagnosis problem (S(T ), ) t (1) 1 r (1) 1 t (2) 1 r (2) 1, t (1) 2 r (1) 2 t (2) 2 r (2) 2, t (1) 3 r (1) 3 t (2) 3 r (2) 3, t (1) r (1) t (2) δ T t 1 :2 r 1 :2 t 2 :2 r 2 :2 t 3 :2 r 3 :2 t 4 :2 r 4 :1 δ t 1 : 2 r 1.OK :n 1 r 1.KO : n 2 t 2 : 2 r 2.OK :n 3 r 2.KO : n 4 t 3 : 2 r 3.OK :n 5 r 3.KO : n 6 t 4 : 2 r 4 : 1 55 / 101

56 Diagnosis problem: D= M 0,(S(T ), ), ˆM (Li et al. [2009a]) Initial marking M 0 p 1 p 2 p 3 p 4 p 11 p 21 p 22 p 32 p 33 p 43 p 44 p 14,,,, 0, 0, 0, 0, 0, 0, 0, 0 Symptom ˆM p 1 p 2 p 3 p 4 p 11 p 21 p 22 p 32 p 33 p 43 p 44 p 14 0,,, 0, 0, 0, 0, 0, 0, 0, b, r A solution for a CPN diagnosis problem (S(T ), ) t (1) 1 r (1) 1 t (2) 1 r (2) 1, t (1) 2 r (1) 2 t (2) 2 r (2) 2, t (1) 3 r (1) 3 t (2) 3 r (2) 3, t (1) r (1) t (2) δ T t 1 :2 r 1 :2 t 2 :2 r 2 :2 t 3 :2 r 3 :2 t 4 :2 r 4 :1 δ t 1 : 2 r 1.OK :n 1 r 1.KO : n 2 t 2 : 2 r 2.OK :n 3 r 2.KO : n 4 t 3 : 2 r 3.OK :n 5 r 3.KO : n 6 t 4 : 2 r 4 : 1 Covering relation: b, r ˆM = M 0 + C δ = ˆM X M0 + C X δ 56 / 101

57 p 14 : r FW(χp 1 ) 1 χp / 101 Inequations system ˆM b r M r C t 1 t 2 t 3 t 1 r 2 r 3 4 OK KO OK KO OK KO r 4 p 1 χp 1 χp 1 FW(χp ) 11 r FW(χp ) 13 p 2 χp 2 χp 2 FW(χp ) 21 r FW(χp ) 22 r FW(χp ) 33 p 3 χp 3 χp 3 FW(χp 32 ) r FW(χp 33 ) r p 4 χp 4 χp 4 FW(χp 43 ) r FW(χp 44 ) p 11 FW(χp ) 1 χp 11 χp 11 p 21 FW(χp ) 2 χp 21 χp 21 p 22 FW(χp ) 2 χp 22 χp 22 p 32 FW(χp ) 3 χp 32 χp 32 p 33 FW(χp ) 3 χp 33 χp 33 p 43 FW(χp ) 4 χp 43 χp 43 p 44 FW(χp ) 4 χp 44 p 14 FW(χp ) 1 χp 14 t 1 : 2 r 1.OK :n 1 r 1.KO :n 2 t 2 : 2 r 2.OK :n 3 r 2.KO :n 4 t 3 : 2 r 3.OK :n 5 r 3.KO :n 6 t 4 : 2 r 4 : 1 n 1 + n 2 =2 n 3 + n 4 =2 n 5 + n 6 =2 Example (Inequations system) n 1 + n 2 = 2 n 3 + n 4 = 2 n 5 + n 6 = 1 p 1 : 0 2 χp 2 1 χp + n 1 1 FW(χp 11 ) + n 2 r + 1 FW(χp ) 14 p 2 : 2 χp 2 2 χp + n 2 1 FW(χp 21 ) + n 2 r + n 3 FW(χp 22 ) + n 4 r p 3 : 2 χp 2 3 χp + n 3 3 FW(χp 32 ) + n 4 r + n 5 FW(χp 33 ) + n 6 r p 4 : 0 2 χp 2 4 χp + n 4 5 FW(χp 43 ) + n 6 r + 1 FW(χp ) 44 p 11 : FW(χp ) n 1 1 χp 11 n 2 χp 11 p 21 : FW(χp ) n 2 1 χp 21 n 2 χp 21 p 22 : FW(χp ) n 2 3 χp 22 n 4 χp 22 p 32 : FW(χp ) n 3 3 χp 32 n 4 χp 32 p 33 : FW(χp ) n 3 5 χp 33 n 6 χp 33 p 43 : FW(χp ) n 4 5 χp 43 n 6 χp 43 p 44 : b FW(χp ) 1 4 χp 44

58 Inequations system 58 / 101

59 Diagnosis algorithm: single fault Sketch 1 to propagate with b tokens 2 to propagate with r tokens 3 to integrate results Example (Inequations system) n 1 + n 2 = 2 n 3 + n 4 = 2 n 5 + n 6 = 1 p 1 : 0 2 χp 2 1 χp + n 1 1 FW(χp 11 ) + n 2 r + 1 FW(χp ) 14 p 2 : 2 χp 2 2 χp + n 2 1 FW(χp 21 ) + n 2 r + n 3 FW(χp 22 ) + n 4 r p 3 : 2 χp 2 3 χp + n 3 3 FW(χp 32 ) + n 4 r + n 5 FW(χp 33 ) + n 6 r p 4 : 0 2 χp 2 4 χp + n 4 5 FW(χp 43 ) + n 6 r + 1 FW(χp ) 44 p 11 : FW(χp ) n 1 1 χp 11 n 2 χp 11 p 21 : FW(χp ) n 2 1 χp 21 n 2 χp 21 p 22 : FW(χp ) n 2 3 χp 22 n 4 χp 22 p 32 : FW(χp ) n 3 3 χp 32 n 4 χp 32 p 33 : FW(χp ) n 3 5 χp 33 n 6 χp 33 p 43 : FW(χp 4 ) n 5 χp 43 n 6 χp 43 p 44 : b FW(χp ) 1 4 χp 44 p 14 : r FW(χp ) 1 1 χp / 101

60 Diagnosis algorithm: single fault Sketch 1 to propagate with b tokens 2 to propagate with r tokens 3 to integrate results Example (Inequations system) n 1 + n 2 = 2 n 3 + n 4 = 2 n 5 + n 6 = 1 p 1 : 0 2 χp 2 1 χp + n 1 1 FW(χp 11 ) + n 2 r + 1 FW(χp ) 14 p 2 : 2 χp 2 2 χp + n 2 1 FW(χp 21 ) + n 2 r + n 3 FW(χp 22 ) + n 4 r p 3 : 2 χp 2 3 χp + n 3 3 FW(χp 32 ) + n 4 r + n 5 FW(χp 33 ) + n 6 r p 4 : 0 2 χp 2 4 χp + n 4 5 FW(χp 43 ) + n 6 r + 1 FW(χp ) 44 p 11 : FW(χp ) n 1 1 χp 11 n 2 χp 11 p 21 : FW(χp ) n 2 1 χp 21 n 2 χp 21 p 22 : FW(χp ) n 2 3 χp 22 n 4 χp 22 p 32 : FW(χp ) n 3 3 χp 32 n 4 χp 32 p 33 : FW(χp ) n 3 5 χp 33 n 6 χp 33 p 43 : FW(χp 4 ) n 5 χp 43 n 6 χp 43 p 44 : b FW(χp 4 ) 1 χp 44 p 14 : r FW(χp 1 ) 1 χp 14 Example (χp 44 = b as a constraint) p 44 = b 60 / 101

61 Diagnosis algorithm: single fault Sketch 1 to propagate with b tokens 2 to propagate with r tokens 3 to integrate results Example (Inequations system) n 1 + n 2 = 2 n 3 + n 4 = 2 n 5 + n 6 = 1 p 1 : 0 2 χp 2 1 χp + n 1 1 FW(χp 11 ) + n 2 r + 1 FW(χp ) 14 p 2 : 2 χp 2 2 χp + n 2 1 FW(χp 21 ) + n 2 r + n 3 FW(χp 22 ) + n 4 r p 3 : 2 χp 2 3 χp + n 3 3 FW(χp 32 ) + n 4 r + n 5 FW(χp 33 ) + n 6 r p 4 : 0 2 χp 2 4 χp + n 4 5 FW(χp 43 ) + n 6 r + 1 FW(χp ) 44 p 11 : FW(χp ) n 1 1 χp 11 n 2 χp 11 p 21 : FW(χp ) n 2 1 χp 21 n 2 χp 21 p 22 : FW(χp ) n 2 3 χp 22 n 4 χp 22 p 32 : FW(χp ) n 3 3 χp 32 n 4 χp 32 p 33 : FW(χp ) n 3 5 χp 33 n 6 χp 33 p 43 : FW(χp 4 ) n 5 χp 43 n 6 χp 43 p 44 : b FW(χp 4 ) 1 χp 44 p 14 : r FW(χp 1 ) 1 χp 14 Example (χp 44 = b as a constraint) p 44 = b p 4 = b 61 / 101

62 Diagnosis algorithm: single fault Sketch 1 to propagate with b tokens 2 to propagate with r tokens 3 to integrate results Example (Inequations system) n 1 + n 2 = 2 n 3 + n 4 = 2 n 5 + n 6 = 1 p 1 : 0 2 χp 2 1 χp + n 1 1 FW(χp 11 ) + n 2 r + 1 FW(χp ) 14 p 2 : 2 χp 2 2 χp + n 2 1 FW(χp 21 ) + n 2 r + n 3 FW(χp 22 ) + n 4 r p 3 : 2 χp 2 3 χp + n 3 3 FW(χp 32 ) + n 4 r + n 5 FW(χp 33 ) + n 6 r p 4 : 0 2 χp 2 4 χp + n 4 5 FW(χp 43 ) + n 6 r + 1 FW(χp ) 44 p 11 : FW(χp ) n 1 1 χp 11 n 2 χp 11 p 21 : FW(χp ) n 2 1 χp 21 n 2 χp 21 p 22 : FW(χp ) n 2 3 χp 22 n 4 χp 22 p 32 : FW(χp ) n 3 3 χp 32 n 4 χp 32 p 33 : FW(χp ) n 3 5 χp 33 n 6 χp 33 p 43 : FW(χp 4 ) n 5 χp 43 n 6 χp 43 p 44 : b FW(χp 4 ) 1 χp 44 p 14 : r FW(χp 1 ) 1 χp 14 Example (χp 44 = b as a constraint) p 44 = b p 4 = b p 43 = b n 6 = 0 62 / 101

63 Diagnosis algorithm: single fault Sketch 1 to propagate with b tokens 2 to propagate with r tokens 3 to integrate results Example (Inequations system) n 1 + n 2 = 2 n 3 + n 4 = 2 n 5 + n 6 = 1 p 1 : 0 2 χp 2 1 χp + n 1 1 FW(χp 11 ) + n 2 r + 1 FW(χp ) 14 p 2 : 2 χp 2 2 χp + n 2 1 FW(χp 21 ) + n 2 r + n 3 FW(χp 22 ) + n 4 r p 3 : 2 χp 2 3 χp + n 3 3 FW(χp 32 ) + n 4 r + n 5 FW(χp 33 ) + n 6 r p 4 : 0 2 χp 2 4 χp + n 4 5 FW(χp 43 ) + n 6 r + 1 FW(χp ) 44 p 11 : FW(χp ) n 1 1 χp 11 n 2 χp 11 p 21 : FW(χp ) n 2 1 χp 21 n 2 χp 21 p 22 : FW(χp ) n 2 3 χp 22 n 4 χp 22 p 32 : FW(χp ) n 3 3 χp 32 n 4 χp 32 p 33 : FW(χp ) n 3 5 χp 33 n 6 χp 33 p 43 : FW(χp 4 ) n 5 χp 43 n 6 χp 43 p 44 : b FW(χp 4 ) 1 χp 44 p 14 : r FW(χp 1 ) 1 χp 14 Example (χp 44 = b as a constraint) p 44 = b p 4 = b p 43 = b n 6 = 0 63 / 101

64 Diagnosis algorithm: single fault Sketch 1 to propagate with b tokens 2 to propagate with r tokens 3 to integrate results Example (Inequations system) n 1 + n 2 = 2 n 3 + n 4 = 2 n 5 + n 6 = 1 p 1 : 0 2 χp 2 1 χp + n 1 1 FW(χp 11 ) + n 2 r + 1 FW(χp ) 14 p 2 : 2 χp 2 2 χp + n 2 1 FW(χp 21 ) + n 2 r + n 3 FW(χp 22 ) + n 4 r p 3 : 2 χp 2 3 χp + n 3 3 FW(χp 32 ) + n 4 r + n 5 FW(χp 33 ) + n 6 r p 4 : 0 2 χp 2 4 χp + n 4 5 FW(χp 43 ) + n 6 r + 1 FW(χp ) 44 p 11 : FW(χp ) n 1 1 χp 11 n 2 χp 11 p 21 : FW(χp ) n 2 1 χp 21 n 2 χp 21 p 22 : FW(χp ) n 2 3 χp 22 n 4 χp 22 p 32 : FW(χp ) n 3 3 χp 32 n 4 χp 32 p 33 : FW(χp ) n 3 5 χp 33 n 6 χp 33 p 43 : FW(χp 4 ) n 5 χp 43 n 6 χp 43 p 44 : b FW(χp 4 ) 1 χp 44 p 14 : r FW(χp 1 ) 1 χp 14 Example (χp 44 = b as a constraint) p 44 = b Example (χp 14 = r) p 14 = r p 4 = b p 43 = b n 6 = 0 64 / 101

65 Diagnosis algorithm: single fault Sketch 1 to propagate with b tokens 2 to propagate with r tokens 3 to integrate results Example (Inequations system) n 1 + n 2 = 2 n 3 + n 4 = 2 n 5 + n 6 = 1 p 1 : 0 2 χp 2 1 χp + n 1 1 FW(χp 11 ) + n 2 r + 1 FW(χp ) 14 p 2 : 2 χp 2 2 χp + n 2 1 FW(χp 21 ) + n 2 r + n 3 FW(χp 22 ) + n 4 r p 3 : 2 χp 2 3 χp + n 3 3 FW(χp 32 ) + n 4 r + n 5 FW(χp 33 ) + n 6 r p 4 : 0 2 χp 2 4 χp + n 4 5 FW(χp 43 ) + n 6 r + 1 FW(χp ) 44 p 11 : FW(χp ) n 1 1 χp 11 n 2 χp 11 p 21 : FW(χp ) n 2 1 χp 21 n 2 χp 21 p 22 : FW(χp ) n 2 3 χp 22 n 4 χp 22 p 32 : FW(χp ) n 3 3 χp 32 n 4 χp 32 p 33 : FW(χp ) n 3 5 χp 33 n 6 χp 33 p 43 : FW(χp 4 ) n 5 χp 43 n 6 χp 43 p 44 : b FW(χp 4 ) 1 χp 44 p 14 : r FW(χp 1 ) 1 χp 14 Example (χp 44 = b as a constraint) p 44 = b Example (χp 14 = r) p 14 = r p 4 = b p 1 = r p 43 = b n 6 = 0 65 / 101

66 Diagnosis algorithm: single fault Sketch 1 to propagate with b tokens 2 to propagate with r tokens 3 to integrate results Example (Inequations system) n 1 + n 2 = 2 n 3 + n 4 = 2 n 5 + n 6 = 1 p 1 : 0 2 χp 2 1 χp + n 1 1 FW(χp 11 ) + n 2 r + 1 FW(χp ) 14 p 2 : 2 χp 2 2 χp + n 2 1 FW(χp 21 ) + n 2 r + n 3 FW(χp 22 ) + n 4 r p 3 : 2 χp 2 3 χp + n 3 3 FW(χp 32 ) + n 4 r + n 5 FW(χp 33 ) + n 6 r p 4 : 0 2 χp 2 4 χp + n 4 5 FW(χp 43 ) + n 6 r + 1 FW(χp ) 44 p 11 : FW(χp ) n 1 1 χp 11 n 2 χp 11 p 21 : FW(χp ) n 2 1 χp 21 n 2 χp 21 p 22 : FW(χp ) n 2 3 χp 22 n 4 χp 22 p 32 : FW(χp ) n 3 3 χp 32 n 4 χp 32 p 33 : FW(χp ) n 3 5 χp 33 n 6 χp 33 p 43 : FW(χp 4 ) n 5 χp 43 n 6 χp 43 p 44 : b FW(χp 4 ) 1 χp 44 p 14 : r FW(χp 1 ) 1 χp 14 Example (χp 44 = b as a constraint) p 44 = b Example (χp 14 = r) p 14 = r p 4 = b p 1 = r p 43 = b n 6 = 0 p11 = r n 2 > 0 66 / 101

67 Diagnosis algorithm: single fault Sketch 1 to propagate with b tokens 2 to propagate with r tokens 3 to integrate results Example (Inequations system) n 1 + n 2 = 2 n 3 + n 4 = 2 n 5 + n 6 = 1 p 1 : 0 2 χp 2 1 χp + n 1 1 FW(χp 11 ) + n 2 r + 1 FW(χp ) 14 p 2 : 2 χp 2 2 χp + n 2 1 FW(χp 21 ) + n 2 r + n 3 FW(χp 22 ) + n 4 r p 3 : 2 χp 2 3 χp + n 3 3 FW(χp 32 ) + n 4 r + n 5 FW(χp 33 ) + n 6 r p 4 : 0 2 χp 2 4 χp + n 4 5 FW(χp 43 ) + n 6 r + 1 FW(χp ) 44 p 11 : FW(χp ) n 1 1 χp 11 n 2 χp 11 p 21 : FW(χp ) n 2 1 χp 21 n 2 χp 21 p 22 : FW(χp ) n 2 3 χp 22 n 4 χp 22 p 32 : FW(χp ) n 3 3 χp 32 n 4 χp 32 p 33 : FW(χp ) n 3 5 χp 33 n 6 χp 33 p 43 : FW(χp 4 ) n 5 χp 43 n 6 χp 43 p 44 : b FW(χp 4 ) 1 χp 44 p 14 : r FW(χp 1 ) 1 χp 14 Example (χp 44 = b as a constraint) p 44 = b Example (χp 14 = r) p 14 = r p 4 = b p 1 = r p 43 = b n 6 = 0 p11 = r n 2 > 0 67 / 101

68 Diagnosis algorithm: single fault Sketch 1 to propagate with b tokens 2 to propagate with r tokens 3 to integrate results Example (Inequations system) n 1 + n 2 = 2 n 3 + n 4 = 2 n 5 + n 6 = 1 p 1 : 0 2 χp 2 1 χp + n 1 1 FW(χp 11 ) + n 2 r + 1 FW(χp ) 14 p 2 : 2 χp 2 2 χp + n 2 1 FW(χp 21 ) + n 2 r + n 3 FW(χp 22 ) + n 4 r p 3 : 2 χp 2 3 χp + n 3 3 FW(χp 32 ) + n 4 r + n 5 FW(χp 33 ) + n 6 r p 4 : 0 2 χp 2 4 χp + n 4 5 FW(χp 43 ) + n 6 r + 1 FW(χp ) 44 p 11 : FW(χp ) n 1 1 χp 11 n 2 χp 11 p 21 : FW(χp ) n 2 1 χp 21 n 2 χp 21 p 22 : FW(χp ) n 2 3 χp 22 n 4 χp 22 p 32 : FW(χp ) n 3 3 χp 32 n 4 χp 32 p 33 : FW(χp ) n 3 5 χp 33 n 6 χp 33 p 43 : FW(χp 4 ) n 5 χp 43 n 6 χp 43 p 44 : b FW(χp 4 ) 1 χp 44 p 14 : r FW(χp 1 ) 1 χp 14 Example (χp 44 = b as a constraint) p 44 = b Example (χp 14 = r) p 14 = r p 4 = b p 1 = r Example (Diagnosis) D 1 = {{p 1 },{r 1.KO}} p 43 = b n 6 = 0 p11 = r n 2 > 0 68 / 101

69 Advantages: cyclic observations handling Sketch 1 to propagate with b tokens 2 to propagate with r tokens 3 to integrate result Example (Inequations system) n 1 + n 2 = 1000 n 3 + n 4 = 1000 n 5 + n 6 = 999 p 1 : χp χp + n 1 1 FW(χp 11 ) + n 2 r FW(χp ) 14 p 2 : 1000 χp χp + n 2 1 FW(χp 21 ) + n 2 r + n 3 FW(χp 22 ) + n 4 r p 3 : 1000 χp χp + n 3 3 FW(χp 32 ) + n 4 r + n 5 FW(χp 33 ) + n 6 r p 4 : χp χp + n 4 5 FW(χp 43 ) + n 6 r FW(χp ) 44 p 11 : FW(χp ) n 1 1 χp 11 n 2 χp 11 p 21 : FW(χp ) n 2 1 χp 21 n 1 χp 21 p 22 : FW(χp ) n 2 3 χp 22 n 4 χp 22 p 32 : FW(χp ) n 3 3 χp 32 n 4 χp 32 p 33 : FW(χp ) n 3 5 χp 33 n 6 χp 33 p 43 : FW(χp ) n 4 5 χp 43 n 6 χp 43 p 44 : b FW(χp 4 ) 999 χp 44 p 14 : r FW(χp 1 ) 999 χp 14 Example (χp 44 = b as a constraint) p 44 = b Example (χp 14 = r) p 14 = r p 4 = b p 1 = r Example (Diagnosis) D 1 = {{p 1 },{r 1.KO}} p 43 = b n 6 = 0 p11 = r n 2 > 0 69 / 101

70 Multi faults diagnosis (Li et al. [2009a]) Cartesian-union operator is an operator that calculates the Cartesian product and then keeps the minimal subsets. 70 / 101

71 Multi faults diagnosis (Li et al. [2009a]) Cartesian-union operator is an operator that calculates the Cartesian product and then keeps the minimal subsets. Example D 1 ={{p 1 },{r 1.KO}} Suppose the 4th philosopher finds faulty cutlery on both sides: a new symptom on p 44 : χ p44 = r D 2 = {{p 4 },{r 3.KO}} D=D 1 D2 ={{p 1, p 4 },{p 1, r 3.KO},{r 1.KO, p 4 },{r 1.KO, r 3.KO}} 71 / 101

72 Opposite example for minimal diagnosis CPN model t 1 t 2 χp 1 χp 1 FW(χp 1 ) p 2 p 1 χp 1 χp 2 t 3 p 3 OK : FW(χp 1 ) KO:r EL(χp 1,χp 2 ) 72 / 101

73 Opposite example for minimal diagnosis Example (S(T ), )) S(T ) = {t 1, t 2, t 2 } t 1 t 3, t 2 t 3 CPN model t 1 t 2 χp 1 χp 1 FW(χp 1 ) p 2 p 1 χp 1 χp 2 t 3 p 3 OK : FW(χp 1 ) KO:r EL(χp 1,χp 2 ) 73 / 101

74 Opposite example for minimal diagnosis Example (S(T ), )) S(T ) = {t 1, t 2, t 2 } t 1 t 3, t 2 t 3 CPN model Example ( δ T ) t 1 t 2 χp 1 χp 1 FW(χp 1 ) OK : FW(χp 1 ) KO:r p 2 p 1 χp 1 χp 2 t 1 t 2 t t 3 EL(χp 1,χp 2 ) p 3 74 / 101

75 Opposite example for minimal diagnosis Example (S(T ), )) S(T ) = {t 1, t 2, t 2 } t 1 t 3, t 2 t 3 CPN model t 1 t 2 χp 1 χp 1 FW(χp 1 ) p 2 p 1 χp 1 χp 2 t 3 p 3 OK : FW(χp 1 ) KO:r EL(χp 1,χp 2 ) Example ( δ T ) t 1 t 2 t Example (Two possible observation traces) 1 t 1 t 2 t 3 : t 2.KO can transmit the fault by r token 2 t 2 t 1 t 3 : the effect of t 2.KO is overwriten by t 1 75 / 101

76 Opposite example for minimal diagnosis Example (S(T ), )) S(T ) = {t 1, t 2, t 2 } t 1 t 3, t 2 t 3 CPN model t 1 t 2 χp 1 χp 1 FW(χp 1 ) p 2 p 1 χp 1 χp 2 t 3 p 3 OK : FW(χp 1 ) KO:r EL(χp 1,χp 2 ) Example ( δ T ) t 1 t 2 t Example (Two possible observation traces) 1 t 1 t 2 t 3 : t 2.KO can transmit the fault by r token 2 t 2 t 1 t 3 : the effect of t 2.KO is overwriten by t 1 Diagnosis D D = {{p 2 },{t 2.KO}} is only minimal only for trace 1 76 / 101

77 Diagnosis minimality vs. precision 77 / 101

78 Architecture of BPEL Monitoring and Diagnosis (WSDIAMOND) 78 / 101

79 Centralized diagnosis solution 79 / 101

80 Decentralized diagnosis architecture (Li et al. [2009b]) 80 / 101

81 Decentralized coordination protocol (Zaitsev [2005]) Result of D i Trigger D i Alarm in BPELi D j provides C with result No D jfor further request Terminate Exists D jfor further request D selected j Trigger D j Diagnoses updated D provides j C with result Result of D j 81 / 101

82 Decentralized coordination protocol (Zaitsev [2005]) Result of D i Trigger D i Alarm in BPELi D j provides C with result No D jfor further request Terminate Exists D jfor further request D selected j Trigger D j Diagnoses updated D provides j C with result Result of D j Equivalence of global and decentralized diagnosis (theorem 2) Diag= Diag j : the solution of the global inequations system is the union C C l j l Diag l of the solutions of the local inequations systems if they are solved according to the affecting order of the bordered places. 82 / 101

83 Diagnosis problem BWS1 5 6 Rec1 1 0 A (d1,d2,m1,m2,c1,c2,con) Rec2 3 2 Inv1 9 (P,ID,cient) B 4 Inv2 (t1,t2,d1,d2,m1,m2,c1,c2,p,id) Inv Rec3 7 Rep1 8 Pick1 Inv C (d1,d2,m1,m2,c1,c2,client,con) BWS3 DB1 Pick2 OM3 OM4 Switch 17 ("Cancel") ("No credit") OM1 OM Inv8 Inv6 16 Inv5 Inv7 DB2 BWS Inv9 23 Rep (d1,d2,m1,m2,c,con,"no credit") Client sent the departure/arrive dates and cities, client info and reservation condition 83 / 101

84 Diagnosis problem BWS1 5 6 Rec1 1 0 A (d1,d2,m1,m2,c1,c2,con) Rec2 3 2 Inv1 9 (P,ID,cient) B 4 Inv2 (t1,t2,d1,d2,m1,m2,c1,c2,p,id) Inv Rec3 7 Rep1 8 Pick1 Inv C (d1,d2,m1,m2,c1,c2,client,con) BWS3 DB1 Pick2 OM3 OM4 Switch 17 ("Cancel") ("No credit") OM1 OM Inv8 Inv6 16 Inv5 Inv7 DB2 BWS Inv9 23 Rep (d1,d2,m1,m2,c,con,"no credit") Travel agency (C) requested the airline company (A) to search for the flights and reserved the most satisfying one 84 / 101

85 Diagnosis problem BWS1 5 6 Rec1 1 0 A (d1,d2,m1,m2,c1,c2,con) Rec2 3 2 Inv1 9 (P,ID,cient) B 4 Inv2 (t1,t2,d1,d2,m1,m2,c1,c2,p,id) Inv Rec3 7 Rep1 8 Pick1 Inv C (d1,d2,m1,m2,c1,c2,client,con) BWS3 DB1 Pick2 OM3 OM4 Switch 17 ("Cancel") ("No credit") OM1 OM Inv8 Inv6 16 Inv5 Inv7 DB2 BWS Inv9 23 Rep (d1,d2,m1,m2,c,con,"no credit") Travel agency (C) requested the payment with bank (B) account 85 / 101

86 Diagnosis problem BWS1 5 6 Rec1 1 0 A (d1,d2,m1,m2,c1,c2,con) Rec2 3 2 Inv1 9 (P,ID,cient) B 4 Inv2 (t1,t2,d1,d2,m1,m2,c1,c2,p,id) Inv Rec3 7 Rep1 8 Pick1 Inv C (d1,d2,m1,m2,c1,c2,client,con) BWS3 DB1 Pick2 OM3 OM4 Switch 17 ("Cancel") ("No credit") OM1 OM Inv8 Inv6 16 Inv5 Inv7 DB2 BWS Inv9 23 Rep (d1,d2,m1,m2,c,con,"no credit") Bank (B) returned "no credit" fault 86 / 101

87 Diagnosis problem BWS1 5 6 Rec1 1 0 A (d1,d2,m1,m2,c1,c2,con) Rec2 3 2 Inv1 9 (P,ID,cient) B 4 Inv2 (t1,t2,d1,d2,m1,m2,c1,c2,p,id) Inv Rec3 7 Rep1 8 Pick1 Inv C (d1,d2,m1,m2,c1,c2,client,con) BWS3 DB1 Pick2 OM3 OM4 Switch 17 ("Cancel") ("No credit") OM1 OM Inv8 Inv6 16 Inv5 Inv7 DB2 BWS Inv9 23 Rep (d1,d2,m1,m2,c,con,"no credit") Travel agency (C) canceled the reservation 87 / 101

88 Diagnosis problem BWS1 5 6 Rec1 1 0 A (d1,d2,m1,m2,c1,c2,con) Rec2 3 2 Inv1 9 (P,ID,cient) B 4 Inv2 (t1,t2,d1,d2,m1,m2,c1,c2,p,id) Inv Rec3 7 Rep1 8 Pick1 Inv C (d1,d2,m1,m2,c1,c2,client,con) BWS3 DB1 Pick2 OM3 OM4 Switch 17 ("Cancel") ("No credit") OM1 OM Inv8 Inv6 16 Inv5 Inv7 DB2 BWS Inv9 23 Rep (d1,d2,m1,m2,c,con,"no credit") Travel agency (C) return a "no credit" fault to client 88 / 101

89 Diagnosis coordination BWS1 5 6 Rec1 1 0 A (d1,d2,m1,m2,c1,c2,con) Rec2 3 2 Inv1 9 (P,ID,cient) B 4 Inv2 (t1,t2,d1,d2,m1,m2,c1,c2,p,id) Inv Rec3 7 Rep1 8 Pick1 Inv C (d1,d2,m1,m2,c1,c2,client,con) BWS3 DB1 Pick2 OM3 OM4 Switch 17 ("Cancel") ("No credit") OM1 OM Inv8 Inv6 16 Inv5 Inv7 DB2 BWS Inv9 23 Rep (d1,d2,m1,m2,c,con,"no credit") Mapping: customer:25->c:24, C:17->B:16, B:15->BWS3:14, BWS3:13->B:12, B:11->C:10, C:9->A:8, A:7->BWS1:6, BWS1:5->A:4, A:3->C:2, C:1->customer:0 89 / 101

90 Diagnosis coordination BWS1 5 6 Rec1 1 0 A (d1,d2,m1,m2,c1,c2,con) Rec2 3 2 Inv1 9 (P,ID,cient) B 4 Inv2 (t1,t2,d1,d2,m1,m2,c1,c2,p,id) Inv Rec3 7 Rep1 8 Pick1 Inv C (d1,d2,m1,m2,c1,c2,client,con) BWS3 DB1 BWS2 Pick2 OM3 OM4 ("Cancel") ("No credit") OM1 OM >17 Inv8 Inv6 16 Inv Inv Rep (d1,d2,m1,m2,c,con,"no credit") Switch Inv7 DB2 Mapping: customer:25->c:24, C:17->B:16, B:15->BWS3:14, BWS3:13->B:12, B:11->C:10, C:9->A:8, A:7->BWS1:6, BWS1:5->A:4, A:3->C:2, C:1->customer:0 90 / 101

91 Diagnosis coordination BWS1 5 6 Rec1 1 0 A (d1,d2,m1,m2,c1,c2,con) Rec2 3 2 Inv1 9 (P,ID,cient) B 4 Inv2 (t1,t2,d1,d2,m1,m2,c1,c2,p,id) Inv Rec >15 Rep1 8 Pick1 15->BSW3 12 Inv >13 C (d1,d2,m1,m2,c1,c2,client,con) BWS3 DB1 BWS2 Pick2 OM3 OM >11 ("Cancel") ("No credit") OM1 OM >17 Inv8 Inv6 16 Inv5 Inv Inv9 23 Rep (d1,d2,m1,m2,c,con,"no credit") Switch 15->12 DB2 Mapping: customer:25->c:24, C:17->B:16, B:15->BWS3:14, BWS3:13->B:12, B:11->C:10, C:9->A:8, A:7->BWS1:6, BWS1:5->A:4, A:3->C:2, C:1->customer:0 91 / 101

92 Diagnosis coordination BWS1 5 6 C (d1,d2,m1,m2,c1,c2,client,con) Rec1 1 0 A (d1,d2,m1,m2,c1,c2,con) >7Rec2 Inv1 9 B 7->BSW1 (P,ID,cient) 4 10->9 Inv2 (t1,t2,d1,d2,m1,m2,c1,c2,p,id) Inv Rec >15 7->5 4->3Rep1 8 Pick1 15->BSW3 12 Inv > BWS3 DB1 BWS2 Pick2 OM3 OM >11 ("Cancel") ("No credit") OM1 OM >17 Inv8 Inv6 16 Inv5 Inv Inv9 23 Rep (d1,d2,m1,m2,c,con,"no credit") Switch 15->12 DB2 Mapping: customer:25->c:24, C:17->B:16, B:15->BWS3:14, BWS3:13->B:12, B:11->C:10, C:9->A:8, A:7->BWS1:6, BWS1:5->A:4, A:3->C:2, C:1->customer:0 92 / 101

93 Diagnosis coordination BWS1 5 6 C (d1,d2,m1,m2,c1,c2,client,con) Rec1 1 0 A (d1,d2,m1,m2,c1,c2,con) >7Rec2 Inv1 9 B 7->BSW1 (P,ID,cient) 4 10->9 Inv2 (t1,t2,d1,d2,m1,m2,c1,c2,p,id) Inv Rec >15 7->5 4->3Rep1 8 Pick1 15->BSW3 12 Inv > BWS3 DB1 BWS2 Pick2 OM3 OM >11 ("Cancel") ("No credit") OM1 OM >17 Inv8 Inv6 16 Inv5 Inv Inv9 23 Rep (d1,d2,m1,m2,c,con,"no credit") Switch 15->12 DB2 Mapping: customer:25->c:24, C:17->B:16, B:15->BWS3:14, BWS3:13->B:12, B:11->C:10, C:9->A:8, A:7->BWS1:6, BWS1:5->A:4, A:3->C:2, C:1->customer:0 93 / 101

94 Diagnosis coordination BWS1 5 6 Rec1 2->1 1 0 A (d1,d2,m1,m2,c1,c2,con) 1-> >7Rec2 Inv1 9 B 7->BSW1 (P,ID,cient) 4 10->9 Inv2 (t1,t2,d1,d2,m1,m2,c1,c2,p,id) Inv Rec >15 7->5 4->3Rep1 8 Pick1 15->BSW3 12 Inv >13 C (d1,d2,m1,m2,c1,c2,client,con) BWS3 DB1 BWS2 Pick2 OM3 OM >11 ("Cancel") ("No credit") OM1 OM >17 Inv8 Inv6 16 Inv5 Inv Inv9 23 Rep (d1,d2,m1,m2,c,con,"no credit") Switch 15->12 DB2 Mapping: customer:25->c:24, C:17->B:16, B:15->BWS3:14, BWS3:13->B:12, B:11->C:10, C:9->A:8, A:7->BWS1:6, BWS1:5->A:4, A:3->C:2, C:1->customer:0 94 / 101

95 Diagnosis coordination BWS1 5 DB1 6 BWS2 A 8->7Rec2 7->BSW1 4 Inv2 7-> >3Rep1 C (d1,d2,m1,m2,c1,c2,con) 1->0 3 2 Inv1 9 B (P,ID,cient) 10->9 Inv Rec3 16->15 Pick1 D={BWS1}, Pick2 OM3 OM4 Switch 15->12 {BWS3}, >11 {d1}, DB2 ("Cancel") ("No credit") {d2}, OM1 OM >17 Inv8 Inv6 16 Inv5 Inv (t1,t2,d1,d2,m1,m2,c1,c2,p,id) 20 Inv9 23 Rec1 2->1 1 Rep (d1,d2,m1,m2,c,con,"no credit") (d1,d2,m1,m2,c1,c2,client,con) 0 15->BSW Inv Result 15->13 BWS3 Mapping: customer:25->c:24, C:17->B:16, B:15->BWS3:14, BWS3:13->B:12, B:11->C:10, C:9->A:8, A:7->BWS1:6, BWS1:5->A:4, A:3->C:2, C:1->customer:0 95 / 101

96 A possible explanation Date format interpreting fault: dd/mm/yyyy vs. mm/dd/yyyy Reservation failed because of no enough credit Input on agency service: on Jul 9, reserved a ticket on Nov 7 and Dec 7 Input on airline service: reserved a ticket on Jul 11 and Jul 12 Tickets were much more expensive on Jul 9 for Jul 11 and Jul 12! 96 / 101

97 Contributions CPN model (Li et al. [2009a]) Places represent the data and control Transition modes represent the correct and faulty system behavior Characteristic vector represents the partially ordered observation Token colors represent the data correctness status: correct (b), faulty (r), unknown ( ) Automatic decentralized diagnosis application Local monitoring components (C#, Java, MySQL by Omar Aaouatif, intern) BPEL2CPN transilator (Java Li et al. [2007],Li et al. [2009a]) Dependency relationships between I/O data for each basic activity: illustrate the faults transmission between data and controls in BPEL Complex variables (XPath) CPN places Basic activities and structural operators translation CPN transitions Local diagnosers and decentralized coordinator (Java) Diagnosis algorithm (Li et al. [2009a],Li et al. [2009b]) Effective off-line diagnosis based on algebraic symbolic calculation Handling cyclic observations in an elegant way Decentralized coordinator protocols 97 / 101