Behavioral comparison of process models based on canonically reduced event structures
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Behavioral Comparison of Process Models Based on Canonically Reduced Event Structures. Paolo Baldan Marlon Dumas Luciano García Abel Armas. Behavioral comparison of process. Explain the differences between a pair of process models using simple and intuitive statements

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Behavioral Comparison of Process Models Based on Canonically Reduced Event Structures

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Behavioral Comparison of Process Models Based on Canonically Reduced Event Structures

Paolo Baldan

Marlon Dumas

Luciano 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

Silent transition

Transition

  • Markings: {{p0}, {p1}, {p2}, …}

  • Firing sequence: {{a,b, …}, …}

  • Executions: {{a,b,c,d}, …}

Place


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 events

    • Lexicographic order on the event’s label

    • Largest set of events

    • 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

    • Relations among matched events

    • In model 2, there is a state after the execution of task cwhere 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

    • 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

    • Unmatched events

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

    • There is an additional occurrence of task cafter 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

    • Consider only common behavior (common labels of tasks)

    • One model can have more behavior than other

      • Error tolerant graph matching techniques

    • Discrepancies

      • Mismatching relations among matched events (approximate context)

      • Mismatching repetitive behavior

      • Unmatched events (approximate context)


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