Behavioral Comparison of Process Models Based on Canonically

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

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

Business process models. Runs BPM 2014 3

Spot the difference! Not structural differences BPM 2014 4

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

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

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

Example PES A D A B A G CC B D E G F B EF D E G GB A C D D E G C F D E G D F E E

Prime vs. Asymmetric event structures Reduction* Prime Event Structure (PES) Asymmetric Event Structure (AES) *Reduction of event structures under hp-bisimulation http: //arxiv. org/abs/1403. 7181. BPM 2014 9

Another example

Reduction and canonicity 1 2 Not canonical • 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

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

Cyclic process models = infinite number of events

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

Comparator Finite representation Canonical Reduction AES 1 Comparator Finite representation BPM 2014 Canonical Reduction AES 2 15

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

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

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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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 a b c a a 0 1 0 b 0 0 1 c 0 0 0 a 1 0 0 0 0 1 0 … BPM 2014 20

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

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