The Difficulty of Replacing an Inclusive OR-Join

Transcription

1 The Difficulty of Replacing an Inclusive OR-Join Cédric Favre and Hagen Völzer

2 Translating an inclusive OR-join Identify customer New customer Existing customer Create customer record Retrieve Customer record Update customer records Check customer status Is gold customer Is not gold customer Deduct 2% of bill Is not gold customer Check eligibility to become gold customer Add free gift Eligible Not eligible Add taxes Can we translate languages which support inclusive OR-join (IOR join) into languages which do not? 2

3 Why is it relevant? Many analysis techniques are based on (free-choice) Petri nets: control-flow analysis, cost estimation, performance analysis, process mining Example: control-flow analysis Check ustomer status Is gold customer Is not gold customer Deduct 2% of bill Is not gold customer Check eligibility to become gold customer Add free gift Eligible Not eligible Add taxes translate analyze Control-flow errors:. feedback Such translation is necessary to enable the use of Petri net based techniques on industrial business process models containing IOR-joins 3

4 Requirements for a translation Example: control-flow analysis Check ustomer status Is gold customer Is not gold customer Deduct 2% of bill Is not gold customer Check eligibility to become gold customer Add free gift Eligible Not eligible Add taxes translate analyze Control-flow errors:. feedback 1. Equivalence (not difficult on its own) Same behavior as original process 2. Size / complexity An exponential blowup of the size of the model is not acceptable 3. Preservation of the original structure The more structure is preserved, the easiest the analysis result can be communicated 4

5 Our work Restricted to acyclic processes Simpler IOR-join semantics Cycles can be factored out (parsing techniques) IOR-joins are often used in acyclic context (e.g. BPEL) Translating an IOR-join? Two replacement techniques and their condition of applicability Many occurrences of IOR-joins can be satisfactorily translated An IOR-join that is difficult to translate No satisfactory translation for some IOR-joins occurrences 5

6 Outline Local replacements Non-local replacements An IOR-join that is difficult to replace 6

7 Acyclic workflow graphs Parallel, exclusive and inclusive gateways + O Workflow graphs without inclusive gateways are isomorphic to freechoice Petri nets New problem: Can an acyclic workflow graph containing an IORjoin be transformed into a workflow graph without IOR-joins? Semantics: XOR-split XOR-join AND-split + + AND-join IOR-split O 7

8 Acyclic IOR-join semantics filled slot A empty slot IOR-join is enabled if At least one slot is filled It is not the case that some token may still arrive on an empty slot 8

9 Acyclic IOR-join semantics filled slot A empty slot IOR-join is enabled if At least one slot is filled It is not the case that some token may still arrive on an empty slot there is a directed path from a token to an empty slot 9

10 Acyclic IOR-join semantics filled slot A empty slot IOR-join is enabled if At least one slot is filled It is not the case that some token may still arrive on an empty slot there is a directed path from a token to an empty slot 10

11 Acyclic IOR-join semantics filled slot A empty slot IOR-join is enabled if At least one slot is filled It is not the case that some token may still arrive on an empty slot there is a directed path from a token to an empty slot The semantics is non-local Enabling depends on tokens that are not at the join 11

12 Outline Local replacements Non-local replacements An IOR-join that is difficult to replace 12

13 A few intuitive replacements Both edges are mutually exclusive Both edges are always concurrent The first two edges are mutually exclusive 13

14 A few intuitive replacements Both edges are mutually exclusive Both edges are always concurrent The first two edges are mutually exclusive When grouped, they are always concurrent with the last 14

15 Local replacement Replacing IOR-join by a sub-graph (only XOR and AND) Keeping the same set of I/O edges Advantages: Intuitive notion of equivalence: replacement must mimic IOR-join Structure preserved: rest of the workflow graph unchanged 15

16 Local replacement Replacing IOR-join by a sub-graph (only XOR and AND) Keeping the same set of I/O edges Advantages: Intuitive notion of equivalence: replacement must mimic IOR-join Structure preserved: rest of the workflow graph unchanged 16

17 Contributions In the paper Characterization of the IOR-joins that can be replaced locally Replacement technique for all locally replaceable IOR-joins Locally replaceable IOR-joins can be identified and replaced 17

18 Local replacement the limit The local replacement is using gateways with local semantics and only using local information The local information is not enough to differentiate: Not enabled Enabled 18

19 Outline Local replacements Non-local replacements An IOR-join that is difficult to replace 19

20 Non-local replacements Idea Transmit the missing information using bridges Non-local replacement = local replacement + bridges 20

21 Simple K-replacement Idea [Kiepuszewski et al., completion of processes] Replace IOR-join by an AND-join For each incoming edge, bridge all the tokens that are lost 21

22 Simple K-replacement Idea [Kiepuszewski et al., completion of processes] Replace IOR-join by an AND-join For each incoming edge, bridge all the tokens that are lost 22

23 Simple K-replacement Idea [Kiepuszewski et al., completion of processes] Replace IOR-join by an AND-join For each incoming edge, bridge all the tokens that are lost 23

24 Simple K-replacement Idea [Kiepuszewski et al., completion of processes] Replace IOR-join by an AND-join For each incoming edge, bridge all the tokens that are lost 24

25 Simple K-replacement problem The replacement is executed during every execution, but some IOR-joins do not Idea Reduce the area of application 25

26 K-replacement - reduced area of application In the paper K-replacement (reduced area of application) A condition of applicability which can be checked in polynomial time We can identify K-replaceable IOR-joins and replace them in polynomial time 26

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28 Outline Local replacements Non-local replacements An IOR-join that is difficult to replace x 28

29 An IOR-join which is difficult to replace Cannot be: locally replaced, K-replaced We will show that the synchronization role played by y cannot be obtained using AND and XOR logic 29

30 The synchronization role of y cannot be replaced z z Question: can we complete the prefix to obtain same behavior Tasks can be copied, edges of the prefix can be bridged In the paper, we show that the prefix cannot be completed using AND and XOR logic 30

31 The prefix cannot be completed t 1 t z t 1 t 2 t 2 Execution properties There exist executions where t 1 and t z execute and, in executions where t 1 and t z are executed, t 1 always executes before t z There is no execution executing t 1, t 2, and t z 31

32 The prefix cannot be completed t z t 1 t z t 1 z t 2 t 2 Execution properties There exist executions where t 1 and t z execute and, in executions where t 1 and t z are executed, t 1 always executes before t z there is a path from t 1 to t z in the completion There is no execution executing t 1, t 2, and t z 32

33 The prefix cannot be completed t z t 1 t z t 1 z t 2 t 2 Execution properties There exist executions where t 1 and t z execute and, in executions where t 1 and t z are executed, t 1 always executes before t z there is a path from t 1 to t z in the completion this path can be executed There is no execution executing t 1, t 2, and t z 33

34 The prefix cannot be completed t z t 1 t z t 1 z t 2 t 2 Execution properties There exist executions where t 1 and t z execute and, in executions where t 1 and t z are executed, t 1 always executes before t z there is a path from t 1 to t z in the completion this path can be executed There is no execution executing t 1, t 2, and t z 34

35 Conclusions from this example t 1 t z t 2 For any notion of equivalence which implies the conservation of the execution properties There exist executions where t 1 and t z execute and, in executions where t 1 and t z are executed, t 1 always executes before t z There is no execution executing t 1, t 2, and t z The prefix cannot be completed: The synchronization role played by an IOR-join cannot, in general, be implemented using XOR and AND gateways 35

36 Summary Contributions: For acyclic processes Characterization of IOR-joins that can be replaced locally and a local replacement technique A non-local replacement technique with its condition of applicability which run in polynomial time Show that a simple processes contains an IOR-join which synchronization role cannot be replaced by XOR and AND logic For some use cases, we have to be careful when we want to apply Petri net based analysis techniques to models that might contain an IOR-join 36