1. On the Step Branching Time Closure
of Free-Choice Petri Nets
FORTE 2014, June 5, Berlin
Stephan Mennicke, J.-W. Schicke-Uffmann, U. Goltz

2. Example: Business Trips
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3. Example: Business Trips
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4. Example: Business Trips
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5. Example: Business Trips
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6. Example: Business Trips
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7. Example: Business Trips
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8. Example: Business Trips
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9. Example: Business Trips
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10. Example: Business Trips
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11. Example: Business Trips
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12. Example: Business Trips
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13. Example: Business Trips
Travel by. . .
Train?
Car?
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14. Example: Business Trips
Travel by. . .
Train?
Car?
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15. Example: Business Trips
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16. Example: Business Trips
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17. Solution: Free-Choice
Free-choice means . . .
choices independent
from system state
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18. Solution: Free-Choice
Free-choice means . . .
choices independent
from system state
two basic net patterns
. . .
. . .
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19. Super Powers of Free-Choice
simple but non-trivial
subclass of Petri nets:
choice
synchronization
concurrency
. . .
. . .
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20. Super Powers of Free-Choice
simple but non-trivial
subclass of Petri nets:
choice
synchronization
concurrency
distributed components
. . .
. . .
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21. Super Powers of Free-Choice
simple but non-trivial
subclass of Petri nets:
choice
synchronization
concurrency
distributed components
efficient analysis
e. g., [Best 1987]
. . .
. . .
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22. Super Powers of Free-Choice
simple but non-trivial
subclass of Petri nets:
choice
synchronization
concurrency
distributed components
efficient analysis
e. g., [Best 1987]
rich applications
e. g., [Desel & Esparza 1995]
. . .
. . .
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23. Questions & Method
1. What are Step Behavioral
Free-Choice Nets?
2. Are business trips weather
dependent, in general?
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24. Questions & Method
1. What are Step Behavioral
Free-Choice Nets?
2. Are business trips weather
dependent, in general?
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25. Questions & Method
1. What are Step Behavioral
Free-Choice Nets?
2. Are business trips weather
dependent, in general?
N Pattern
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26. Questions & Method
1. What are Step Behavioral
Free-Choice Nets?
2. Are business trips weather
dependent, in general?
Premises
Petri nets N = (P, T, F, M0)
step firing rule
structural conflict nets
step branching time
N Pattern
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27. Roadmap
FC
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28. Roadmap
FC EFC
EFC-nets are FC-nets
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29. Roadmap
FC EFC
EFC-nets are FC-nets up to interleaving
branching time [Best & Shields 1983]
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30. Extended Free-Choice Nets
conflict implies sharing of
resources
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31. Extended Free-Choice Nets
conflict implies sharing of
resources
⇒ choices independent from
system state
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32. Extended Free-Choice Nets
conflict implies sharing of
resources
⇒ choices independent from
system state
⇒ free-choice
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33. Extended Free-Choice Nets
conflict implies sharing of
resources
⇒ choices independent from
system state
⇒ free-choice
but not free-choice Petri nets
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34. FC-Implementation of EFC-Nets
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35. FC-Implementation of EFC-Nets
Procedure
1. Cluster
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36. FC-Implementation of EFC-Nets
Procedure
1. Cluster
2. Split-up
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37. FC-Implementation of EFC-Nets
Procedure
1. Cluster
2. Split-up
3. Synchronize
τ
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38. FC-Implementation of EFC-Nets
Procedure
1. Cluster
2. Split-up
3. Synchronize
4. Choice
τ
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39. Results on EFC-Nets
Theorem
The construction respects step branching time.
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40. Results on EFC-Nets
Theorem
The construction respects step branching time.
clustered transitions are not concurrent
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41. Results on EFC-Nets
Theorem
The construction respects step branching time.
clustered transitions are not concurrent
distinct clusters are not in conflict
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42. Results on EFC-Nets
Theorem
The construction respects step branching time.
clustered transitions are not concurrent
distinct clusters are not in conflict
⇒ step branching structure invariant
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43. Results on EFC-Nets
Theorem
The construction respects step branching time.
clustered transitions are not concurrent
distinct clusters are not in conflict
⇒ step branching structure invariant
τ-steps introduced
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44. Results on EFC-Nets
Theorem
The construction respects step branching time.
clustered transitions are not concurrent
distinct clusters are not in conflict
⇒ step branching structure invariant
τ-steps introduced
⇒ weak step bisimilarity
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45. Results on EFC-Nets
Theorem
The construction respects step branching time.
clustered transitions are not concurrent
distinct clusters are not in conflict
⇒ step branching structure invariant
τ-steps introduced
⇒ weak step bisimilarity
Result
EFC-nets are FC-nets up to step branching time.
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46. Roadmap
FC EFC
EFC-nets are FC-nets up to
interleaving branching time [Best & Shields 1983]
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47. Roadmap
FC EFC BFC
BFC-nets are EFC-nets are FC-nets up to
interleaving branching time [Best & Shields 1983]
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48. Behavioral Free-Choice Nets
conflict implies mutual
activation
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49. Behavioral Free-Choice Nets
conflict implies mutual
activation
choices always occur in the
same way
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50. Behavioral Free-Choice Nets
conflict implies mutual
activation
choices always occur in the
same way
⇒ choices independent from
system state
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51. Behavioral Free-Choice Nets
conflict implies mutual
activation
choices always occur in the
same way
⇒ choices independent from
system state
⇒ free-choice
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52. Behavioral Free-Choice Nets
conflict implies mutual
activation
choices always occur in the
same way
⇒ choices independent from
system state
⇒ free-choice
but not (extended)
free-choice Petri nets
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53. EFC-Implementation of BFC-Nets
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54. EFC-Implementation of BFC-Nets
Procedure
1. Cluster
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55. EFC-Implementation of BFC-Nets
Procedure
1. Cluster
2. Depend
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56. EFC-Implementation of BFC-Nets
Procedure
1. Cluster
2. Depend
3. Fix
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57. BFC Nets & BFC Clustering
cluster transitivity
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58. BFC Nets & BFC Clustering
cluster transitivity
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59. BFC Nets & BFC Clustering
cluster transitivity
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60. BFC Nets & BFC Clustering
cluster transitivity
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61. BFC Nets & BFC Clustering
cluster transitivity
concurrency
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62. BFC Nets & BFC Clustering
cluster transitivity
concurrency
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63. BFC Nets & BFC Clustering
cluster transitivity
concurrency
Impl. from [van Glabbeek et al. 2009]
There is no step branching time equivalent FC Petri
net to the one above.
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64. BFC Nets & BFC Clustering
cluster transitivity
concurrency
Impl. from [van Glabbeek et al. 2009]
There is no step branching time equivalent FC Petri
net to the one above.
Success for BFC nets
without self-loops (LF-BFC)
that are asymmetric choice nets (BFC-AC)
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65. Roadmap Revisited
FC EFC BFC
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66. Roadmap Revisited
FC EFC BFC
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67. Roadmap Revisited
FC EFC BFC
?
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68. What about the N?
t u
two conflicting transitions
two enabledness situations
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69. What about the N?
t u
two conflicting transitions
two enabledness situations
N Characterized
M0
σ1
=⇒ M1
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70. What about the N?
t u
two conflicting transitions
two enabledness situations
N Characterized
M0
σ1
=⇒ M1, M0
σ2
=⇒ M2
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71. What about the N?
t u
two conflicting transitions
two enabledness situations
N Characterized
M0
σ1
=⇒ M1, M0
σ2
=⇒ M2
in M1: {t} does not fail
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72. What about the N?
t u
two conflicting transitions
two enabledness situations
N Characterized
M0
σ1
=⇒ M1, M0
σ2
=⇒ M2
in M1: {t} does not fail
in M1: {u} does fail
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73. What about the N?
t u
two conflicting transitions
two enabledness situations
N Characterized
M0
σ1
=⇒ M1, M0
σ2
=⇒ M2
in M1: {t} does not fail
in M1: {u} does fail
in M2: {t} and {u} do not fail
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74. What about the N?
t u
two conflicting transitions
two enabledness situations
N Characterized
M0
σ1
=⇒ M1, M0
σ2
=⇒ M2
in M1: {t} does not fail
in M1: {u} does fail
in M2: {t} and {u} do not fail
in M2: {t, u} does fail
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75. What about the N?
two conflicting transitions
two enabledness situations
N Characterized
M0
σ1
=⇒ M1, M0
σ2
=⇒ M2
in M1: {t} does not fail
in M1: {u} does fail
in M2: {t} and {u} do not fail
in M2: {t, u} does fail
t u
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76. What about the N?
two conflicting transitions
two enabledness situations
N Characterized
M0
σ1
=⇒ M1, M0
σ2
=⇒ M2
in M1: {t} does not fail
in M1: {u} does fail
in M2: {t} and {u} do not fail
in M2: {t, u} does fail
t u
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77. What about the N?
two conflicting transitions
two enabledness situations
N Characterized
M0
σ1
=⇒ M1, M0
σ2
=⇒ M2
in M1: {t} does not fail
in M1: {u} does fail
in M2: {t} and {u} do not fail
in M2: {t, u} does fail
t u
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78. What about the N?
two conflicting transitions
two enabledness situations
N Characterized
M0
σ1
=⇒ M1, M0
σ2
=⇒ M2
in M1: {t} does not fail
in M1: {u} does fail
in M2: {t} and {u} do not fail
in M2: {t, u} does fail
t u
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79. What about the N?
two conflicting transitions
two enabledness situations
N Characterized
M0
σ1
=⇒ M1, M0
σ2
=⇒ M2
in M1: {t} does not fail
in M1: {u} does fail
in M2: {t} and {u} do not fail
in M2: {t, u} does fail
t u
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80. What have we seen?
FC EFC
LF-BFC
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81. What have we seen?
FC EFC
LF-BFC
BFC-AC
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82. What have we seen?
FC EFC
LF-BFC
BFC-AC
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83. What have we seen?
M
FC EFC
LF-BFC
BFC-AC
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84. What have we seen?
N M
FC EFC
LF-BFC
BFC-AC
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85. Next to come
N M
FC EFC
LF-BFC
BFC-AC
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86. Next to come
N M
FC EFC
LF-BFC
BFC-AC
Thank You!
Stephan Mennicke
mennicke@ips.cs.tu-bs.de
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