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Behavioral Comparison of Process Models Based on Canonically Reduced Event Structures Abel Armas-Cervantes Paolo Baldan Marlon Dumas Luciano García-Bañuelos BPM 2014 1

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Business process models BPM 2014 2 Start event Activity XOR gateway AND gateway End event Run

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Business process models. Runs BPM 2014 3

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Spot the difference! BPM 2014 4 Not structural differences

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Spot the difference! BPM 2014 5 It is possible to execute task Monitor delivery right after Handle bank transfer in model 1 but not in model 2.

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Desiderata Diagnostics: Differences explained with intuitive statements. E.g., – “It is possible to execute task A after B in model 1 but not in model 2.” Semantics: Well-accepted notion of equivalence – Our choice: Configuration equivalence (True-concurrency spectrum) BPM 2014 6

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Event structures Event structures (ES) as the behavioral representations – Events: occurrences of actions – Relations over the events: behavior dependencies observed between pairs of events Prime event structures (PES) – Three relations: conflict, causality and concurrency

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Example PES A B C A B C D E F G F D D E E G A BC DE G FD G E A BC DE G FD G E C G E

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Prime vs. Asymmetric event structures BPM 2014 9 Prime Event Structure (PES)Asymmetric Event Structure (AES) Reduction* *Reduction of event structures under hp-bisimulation http://arxiv.org/abs/1403.7181.

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Another example

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Reduction and canonicity Fist contribution: Deterministic order defining a canonical representation Elements: – Lexicographic order of event labels – Size of the set of events to be merged –... not enough! BPM 2014 11 12 Not canonical

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Deterministic folding Compute combinable set of events Folding order 1.Lexicographic order on the event’s label 2.Size of the set of events to merge 3.Lexicographic order w.r.t. the canonical labels BPM 2014 12

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Cyclic process models = infinite number of events

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Our unfolding Second contribution: Unfolding technique to capture all causal dependencies between tasks – We can distinguish repetitive behavior from non-repetitive BPM 2014 14

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Comparator BPM 2014 15 Comparator AES2AES1 Finite representation Canonical Reduction Finite representation Canonical Reduction

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Comparator(2) Error correcting graph matching techniques for finding similar behavior. – Isomorphism would imply equivalence BPM 2014 16

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Comparator(3) Mismatching relations between matched events – In model 2, there is a state after the execution of task c where d and c are mutually exclusive; whereas in model 1, there is a state after the execution of b where c can occur before d, or c can be skipped Mismatching repetitive behavior – Task b may occur 0 or more times in model 2; whereas in model 1, it occurs at most once Unmatched events – There is an additional occurrence of task b after c in model 2 BPM 2014 17

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Summary Technique for a behavioral comparison of process models using AES – Canonical folding of AES – Finite representation using Petri net unfoldings Characterization of cyclic behavior according to task repetitions – Propose a comparison technique of AES BPM 2014 18

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BPM 2014 19

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Canonical graph label Compute the adjacency matrix of the graph and all its possible permutations Select the largest lexicographical exemplar of the string representation of the permutations – Nauty, a tool to compute canonical graph labeling BPM 2014 20 abc a010 b001 c000 010100000 … bca b010 c000 a100 010000001

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Complete prefix unfolding Truncating techniques based on markings – McMillan and Esparza et al They do not capture all possible causal dependencies BPM 2014 21

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Current limitations Silent transitions can lead to different prefix unfoldings, even though the processes are equivalent BPM 2014 22

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