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 ID: 233558
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Slide1
Behavioral Comparison of Process Models Based on Canonically Reduced Event Structures
Paolo
Baldan
Marlon Dumas
Luciano
García
Abel ArmasSlide2
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 PESSlide3
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 discrepanciesError tolerant graph matching techniques Categorization of discrepanciesSlide4
Background. Petri netsSlide5
Background. Petri nets
Markings
: {{p
0
}, {p
1}, {p2}, …}Firing sequence: {{a,b, …}, …}Executions: {{a,b,c,d}, …}
Place
Transition
Silent transitionSlide6
Background(2). Branching process and PES
Configurations: {{a},
{
a,b
}, {a,c}, {a,b,c}, …}Slide7
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-canonicitySlide8
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 matrixKeep the order given to the vertices in the largest exemplarCompute the canonical graph labeling for PESWeight of the eventsSlide9
Canonical folding
Folding of events
Lexicographic order on the event’s label
Largest set of events
Largest weights
w.r.t. the canonical graph labelingSlide10
Cyclic process models
Infinite number of events in branching process
Infinite number of events in PES
Finite complete prefix
unfoldingsSlide11
Finite complete prefix unfolding
McMillan and Esparza
Truncating techniques based on markings
Does not reflect all the possible causal predecessors for any eventSlide12
Customized complete prefix unfolding
Khomenko
et al. proposes a framework
to define a customized complete prefix
unfolding
Order for configurationsSet of configurationsEquivalenceEquivalence for capturing causal dependenciesSame markingsThe marking was generated by the firing of the same transitionsSlide13
Customized complete prefix unfolding(2)
Cyclic behavior
:
A transition
c
is part of cyclic behavior if there is a configuration with two occurrences of cTransition c is repeated 1 or more times if it occurs in all runs
Transition c is repeated 0 or more times i
f
it does not occur in all
runsSlide14
Not canonical unfolding
It does not guarantee a canonical complete prefix unfolding for equivalent models (
pomset
-trace equivalence)Slide15
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
2Slide16
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 repetitionsCategorization of discrepancies for offering a more understandable feedbackSlide17
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 concurrencySlide18Slide19
Comparison
Consider only common behavior (common labels of tasks)
One model can have more behavior than other
Error
tolerant graph matching techniques
DiscrepanciesMismatching relations among matched events (approximate context)Mismatching
repetitive behaviorUnmatched events (
approximate context
)