Behavioral Comparison of Process Models Based on Canonically

Reduced Event StructuresPaolo Baldan

Marlon DumasLuciano García

Abel Armas

Behavioral comparison of process

• Explain the differences between a pair of process models using simple and intuitive statements

• Abstract representations based on binary behavioral relations– Event structures, e.g., PES and AES

• More expressive formalisms can give smaller representations– AES can provide smaller representations than PES

Comparison based on reduced AES

• Folding technique does not ensure canonicity– Canonical graph labeling technique

• Process models can represent infinite behavior. I.e., cyclic behavior. – Unfolding technique for computing a

finite representation

• Provide understandable feedback about behavioral discrepancies– Error tolerant graph matching

techniques – Categorization of discrepancies

Background. Petri nets

Background. Petri nets

• Markings: {{p0}, {p1}, {p2}, …}• Firing sequence: {{a,b, …}, …}• Executions: {{a,b,c,d}, …}

Place

Transition Silent transition

Background(2). Branching process and PES

Configurations: {{a}, {a,b}, {a,c}, {a,b,c}, …}

Background(3). PES and AES

• AES is a more expressive formalism than PES– Same configurations as PES, but fewer events

– Reduction technique (folding)• hp-bisimilarity

– Non-canonicity

Canonical graph labeling technique

• Canonical graph labeling techniques (McKay‘s algorithm)– Associates a graph with a canonical label

• Largest lexicographical exemplar of the (string linear representation) adjacency matrix

• Keep the order given to the vertices in the largest exemplar

• Compute the canonical graph labeling for PES• Weight of the events

Canonical folding

• Folding of events1. Lexicographic order on the event’s label2. Largest set of events3. Largest weights w.r.t. the canonical graph labeling

Cyclic process models

• Infinite number of events in branching process

• Infinite number of events in PES

• Finite complete prefix unfoldings

Finite complete prefix unfolding

• McMillan and Esparza – Truncating techniques based on markings

• Does not reflect all the possible causal predecessors for any event

Customized complete prefix unfolding

• Khomenko et al. proposes a framework to define a customized complete prefix unfolding

• Order for configurations• Set of configurations• Equivalence

• Equivalence for capturing causal dependencies– Same markings– The marking was generated by the firing of the same

transitions

Customized complete prefix unfolding(2)

• Cyclic behavior:– A transition c is part of cyclic

behavior if there is a configuration with two occurrences of c

– Transition c is repeated 1 or more times if it occurs in all runs

– Transition c is repeated 0 or more times if it does not occur in all runs

Not canonical unfolding

• It does not guarantee a canonical complete prefix unfolding for equivalent models (pomset-trace equivalence)

Comparison

Mismatching repetitive behavior• Task b may occur many times in model 2; whereas in model 1, it is not repeated any

time

• Task c may occur many times in model 2; whereas in model 1, it is not repeated any time

Relations among 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

• In model 2, there is a state after the execution of task a where c can occur before d, or c can be skipped; whereas in model 1, there is a state after the execution of a where c precedes d

Unmatched events• There is an additional occurrence of task b after c in model 2

• There is an additional occurrence of task c after b in model 2

Conclusions

• 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

– Categorization of discrepancies for offering a more understandable feedback

Future work

• Visualization of discrepancies in the models

• Empirical evaluation of the usefulness of diagnostics using real-world process models

• Test if a more refined feedback can be given by using other models of concurrency

Comparison

1. Consider only common behavior (common labels of tasks)

2. One model can have more behavior than other– Error tolerant graph matching techniques

3. Discrepancies1. Mismatching relations among matched events (approximate

context)2. Mismatching repetitive behavior3. Unmatched events (approximate context)