Soundness of Data-Aware Processes with Arithmetic Conditions
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The document discusses the soundness of data-aware processes in information systems, focusing on static and dynamic constraints in process-oriented views. It examines various models, including data petri nets, for soundness checking with arithmetic conditions and explores the challenges of reachability and decidability. The paper highlights advancements in methodologies for formal analysis and practical applications, including improvements in scalability and performance.
![A process model with case data and conditions
Adapted from [Mannhardt et al., Computing 2016]
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![Adapted from [Mannhardt et al., Computing 2016]
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expenses ds dp dj
A process model with case data and conditions](https://image.slidesharecdn.com/caise-2022-dpn-arithmetics-220819230134-968fb223/85/Soundness-of-Data-Aware-Processes-with-Arithmetic-Conditions-7-320.jpg)
![Adapted from [Mannhardt et al., Computing 2016]
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received
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fi
ne
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prefecture
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fi
cation
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prefecture
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prefecture
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amount total
amount
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deducted
expenses ds dp dj
dj
A process model with case data and conditions
x
xw
xr](https://image.slidesharecdn.com/caise-2022-dpn-arithmetics-220819230134-968fb223/85/Soundness-of-Data-Aware-Processes-with-Arithmetic-Conditions-8-320.jpg)
![Adapted from [Mannhardt et al., Computing 2016]
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ne
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prefecture
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aw
, tw
, dw
, pw
≥ 0
pw
≥ 0
0 ≤ dsw
≤ 90days ∧ ew
≥ 0
pw
≥ 0 pw
≥ 0 aw
≥ 0
tr
≥ ar
+ er
dr
≠ 0 ∨ (pr
= 0 ∧ tr
≥ ar
)
t
r
<
a
r
+
e
r
tr
≥ ar
+ er
0 ≤ djw
≤ 60days ∧ dw
≥ 0
d
r
=
0
dr
= 2
0 ≤ dpw
≤ 60days dw
≥ 0 dr
= 0
dr
= 1
amount total
amount
dismissal
code
points
deducted
expenses ds dp dj
A process model with case data and conditions](https://image.slidesharecdn.com/caise-2022-dpn-arithmetics-220819230134-968fb223/85/Soundness-of-Data-Aware-Processes-with-Arithmetic-Conditions-9-320.jpg)
![Data Petri Nets
[Mannhardt,PhD2018; _____,ER2018; _____,ACSD2019]
• Petri nets enriched with typed variables
(ranging over in
fi
nite domains)
• Transitions access variables via read and
write guards
• State: marking + variable assignment
• Transition
fi
ring: usual
fi
ring semantics +
variable assignment update given a binding
for the written variables
In
fi
nite reachability graph even when the net is bounded
Which language to express conditions? We want (linear) arithmetic](https://image.slidesharecdn.com/caise-2022-dpn-arithmetics-220819230134-968fb223/85/Soundness-of-Data-Aware-Processes-with-Arithmetic-Conditions-14-320.jpg)
![Data-Aware Soundness for Data Petri nets
[____,ER2018;____,ACSD2019]
Always “option to complete”:
• There are no dead tasks
• The
fi
nal marking is only reached in a clean way for
some variable assignment
• In every reachable marking, it must be possible to
reach the
fi
nal marking for some variable assignment](https://image.slidesharecdn.com/caise-2022-dpn-arithmetics-220819230134-968fb223/85/Soundness-of-Data-Aware-Processes-with-Arithmetic-Conditions-18-320.jpg)
![A tale of encodings
Reachability
graph
(in
fi
nite-state)
bounded
Data Petri
Net
DDS
(Transition
system with
guards on
edges)
Interleaving
Sound?
Constraint
graph
Symbolic states
Sound?
[ER2018]: variable-to-constant
[ACSD2019]: variable-to-variable
no arithmetic
Direct,
fi
nite abstractions!](https://image.slidesharecdn.com/caise-2022-dpn-arithmetics-220819230134-968fb223/85/Soundness-of-Data-Aware-Processes-with-Arithmetic-Conditions-23-320.jpg)
![A tale of encodings
Reachability
graph
(in
fi
nite-state)
bounded
Data Petri
Net
DDS
(Transition
system with
guards on
edges)
Interleaving
Sound?
Constraint
graph
Symbolic states
Sound?
φ
SMT solvers!
[AAAI2022]
Semantic notion of
fi
nite-summary
Identi
fi
ed syntactic
classes inducing
fi
nite-
summary
Linear-time properties
Requirements
Decidable SAT
on guards
Finite formula](https://image.slidesharecdn.com/caise-2022-dpn-arithmetics-220819230134-968fb223/85/Soundness-of-Data-Aware-Processes-with-Arithmetic-Conditions-26-320.jpg)
![General framework for DPNs with arithmetic
Formal analysis paired with data abstraction techniques
No ad-hoc algorithms: SMT as a Swiss Army knife
Recent progress: CTL* model checking [IJCAR22]
SMT for discovery, tight discovery-reasoning integration
On-
fi
eld validation?](https://image.slidesharecdn.com/caise-2022-dpn-arithmetics-220819230134-968fb223/85/Soundness-of-Data-Aware-Processes-with-Arithmetic-Conditions-39-320.jpg)
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More from Faculty of Computer Science - Free University of Bozen-Bolzano (20)
Soundness of Data-Aware Processes with Arithmetic Conditions
- 1. Paolo Felli, Marco Montali, Sarah Winkler Soundness of data-aware processes with arithmetic conditions CAiSE 2022, Leuven
- 2. Starting point A holistic view of information systems static constraints dynamic constraints data processes
- 3. Starting point A holistic view of information systems static constraints dynamic constraints data processes
- 4. Starting point A holistic view of information systems static constraints dynamic constraints data processes Process-oriented view: “data-aware processes” Formal foundations: execution semantics, analysis, correctness guarantees
- 5. The zoo of data-aware processes Control- fl ow • Petri nets, condition-action rules, declarative constraints,… Data • Variables, relational, semi-structured, with constraints, with read-only data, ontologies, … Integration • Data access, query, manipulation, external inputs, …
- 6. A process model with case data and conditions Adapted from [Mannhardt et al., Computing 2016] Fine received Send fi ne Appeal to prefecture Pay Insert noti fi cation Pay Appeal to judge Pay Send to prefecture Result prefecture Notify Collect credit Add penalty
- 7. Adapted from [Mannhardt et al., Computing 2016] Fine received Send fi ne Appeal to prefecture Pay Insert noti fi cation Pay Appeal to judge Pay Send to prefecture Result prefecture Notify Collect credit Add penalty amount total amount dismissal code points deducted expenses ds dp dj A process model with case data and conditions
- 8. Adapted from [Mannhardt et al., Computing 2016] Fine received Send fi ne Appeal to prefecture Pay Insert noti fi cation Pay Appeal to judge Pay Send to prefecture Result prefecture Notify Collect credit Add penalty amount total amount dismissal code points deducted expenses ds dp dj dj A process model with case data and conditions x xw xr
- 9. Adapted from [Mannhardt et al., Computing 2016] Fine received Send fi ne Appeal to prefecture Pay Insert noti fi cation Pay Appeal to judge Pay Send to prefecture Result prefecture Notify Collect credit Add penalty aw , tw , dw , pw ≥ 0 pw ≥ 0 0 ≤ dsw ≤ 90days ∧ ew ≥ 0 pw ≥ 0 pw ≥ 0 aw ≥ 0 tr ≥ ar + er dr ≠ 0 ∨ (pr = 0 ∧ tr ≥ ar ) t r < a r + e r tr ≥ ar + er 0 ≤ djw ≤ 60days ∧ dw ≥ 0 d r = 0 dr = 2 0 ≤ dpw ≤ 60days dw ≥ 0 dr = 0 dr = 1 amount total amount dismissal code points deducted expenses ds dp dj A process model with case data and conditions
- 10. Mining Modelling
- 11. Fine received Send fi ne Appeal to prefecture Pay Insert noti fi cation Pay Appeal to judge Pay Notify Collect credit Add penalty aw , tw , dw , pw ≥ 0 pw ≥ 0 0 ≤ dsw ≤ 90days ∧ ew ≥ 0 pw ≥ 0 pw ≥ 0 aw ≥ 0 tr ≥ ar + er dr ≠ 0 ∨ (pr = 0 ∧ tr ≥ ar ) t r < a r + e r tr ≥ ar + er 0 ≤ djw ≤ 60days ∧ dw ≥ 0 d r = 0 dr = 2 0 ≤ dpw ≤ 60days Is the model “correct”? Send to prefecture Result prefecture dw ≥ 0 dr = 0 dr = 1
- 12. Fine received Send fi ne Appeal to prefecture Pay Insert noti fi cation Pay Appeal to judge Pay Notify Collect credit Add penalty aw , tw , dw , pw ≥ 0 pw ≥ 0 0 ≤ dsw ≤ 90days ∧ ew ≥ 0 pw ≥ 0 pw ≥ 0 aw ≥ 0 tr ≥ ar + er dr ≠ 0 ∨ (pr = 0 ∧ tr ≥ ar ) t r < a r + e r tr ≥ ar + er 0 ≤ djw ≤ 60days ∧ dw ≥ 0 d r = 0 dr = 2 0 ≤ dpw ≤ 60days Is the model “correct”? Send to prefecture Result prefecture dw ≥ 0 dr = 0 dr = 1 Send to prefecture Result prefecture dr = 0 dr = 1 dw ≥ 0
- 13. Fine received Send fi ne Appeal to prefecture Pay Insert noti fi cation Pay Appeal to judge Pay Notify Collect credit Add penalty aw , tw , dw , pw ≥ 0 pw ≥ 0 0 ≤ dsw ≤ 90days ∧ ew ≥ 0 pw ≥ 0 pw ≥ 0 aw ≥ 0 tr ≥ ar + er dr ≠ 0 ∨ (pr = 0 ∧ tr ≥ ar ) t r < a r + e r tr ≥ ar + er 0 ≤ djw ≤ 60days ∧ dw ≥ 0 d r = 0 dr = 2 0 ≤ dpw ≤ 60days Is the model “correct”? Send to prefecture Result prefecture dw ≥ 0 dr = 0 dr = 1 Send to prefecture Result prefecture dr = 0 dr = 1 dw ≥ 0 Stuck if “send to prefecture” writes d > 1
- 14. Data Petri Nets [Mannhardt,PhD2018; _____,ER2018; _____,ACSD2019] • Petri nets enriched with typed variables (ranging over in fi nite domains) • Transitions access variables via read and write guards • State: marking + variable assignment • Transition fi ring: usual fi ring semantics + variable assignment update given a binding for the written variables In fi nite reachability graph even when the net is bounded Which language to express conditions? We want (linear) arithmetic
- 15. Fragile setting: undecidability around the corner!
- 16. Soundness for Petri nets Always “option to complete”: • There are no dead tasks • The fi nal marking is only reached in a clean way • In every reachable marking, it must be possible to reach the fi nal marking
- 17. Soundness for Petri nets Always “option to complete”: • There are no dead tasks • The fi nal marking is only reached in a clean way • In every reachable marking, it must be possible to reach the fi nal marking Reachability Reachability Branching property
- 18. Data-Aware Soundness for Data Petri nets [____,ER2018;____,ACSD2019] Always “option to complete”: • There are no dead tasks • The fi nal marking is only reached in a clean way for some variable assignment • In every reachable marking, it must be possible to reach the fi nal marking for some variable assignment
- 19. Key questions… 1.Soundness checking decidable for DPNs equipped with arithmetic? 2.Is there an operational way to conduct the check? 3.Is this operational way e ff ective from the computational point of view?
- 20. A tale of encodings bounded Data Petri Net
- 21. A tale of encodings Reachability graph (in fi nite-state) bounded Data Petri Net DDS (Transition system with guards on edges) Interleaving Sound?
- 22. A tale of encodings Reachability graph (in fi nite-state) bounded Data Petri Net DDS (Transition system with guards on edges) Interleaving Sound? Constraint graph Symbolic states Sound?
- 23. A tale of encodings Reachability graph (in fi nite-state) bounded Data Petri Net DDS (Transition system with guards on edges) Interleaving Sound? Constraint graph Symbolic states Sound? [ER2018]: variable-to-constant [ACSD2019]: variable-to-variable no arithmetic Direct, fi nite abstractions!
- 24. A tale of encodings Reachability graph (in fi nite-state) bounded Data Petri Net DDS (Transition system with guards on edges) Interleaving Sound? Constraint graph Symbolic states Sound? φ
- 25. A tale of encodings Reachability graph (in fi nite-state) bounded Data Petri Net DDS (Transition system with guards on edges) Interleaving Sound? Constraint graph Symbolic states Sound? φ SMT solvers! Requirements Decidable SAT on guards Finite formula
- 26. A tale of encodings Reachability graph (in fi nite-state) bounded Data Petri Net DDS (Transition system with guards on edges) Interleaving Sound? Constraint graph Symbolic states Sound? φ SMT solvers! [AAAI2022] Semantic notion of fi nite-summary Identi fi ed syntactic classes inducing fi nite- summary Linear-time properties Requirements Decidable SAT on guards Finite formula
- 27. In this paper… bounded Data Petri Net φ Data-aware soundness • There are no dead tasks • The fi nal marking is only reached in a clean way for some variable assignment • In every reachable marking, it must be possible to reach the fi nal marking for some variable assignment
- 28. In this paper… bounded Data Petri Net φ Data-aware soundness • There are no dead tasks • The fi nal marking is only reached in a clean way for some variable assignment • In every reachable marking, it must be possible to reach the fi nal marking for some variable assignment φ1 φ2 φ3
- 29. In this paper… bounded Data Petri Net φ Data-aware soundness • There are no dead tasks • The fi nal marking is only reached in a clean way for some variable assignment • In every reachable marking, it must be possible to reach the fi nal marking for some variable assignment φ1 φ2 φ3 SMT
- 30. In this paper… bounded Data Petri Net φ Data-aware soundness • There are no dead tasks • The fi nal marking is only reached in a clean way for some variable assignment • In every reachable marking, it must be possible to reach the fi nal marking for some variable assignment φ1 φ2 φ3 SMT For general linear arithmetic: no guarantees Guarantees for classes identi fi ed in AAAI22 (includes all previous results) The example before falls in one of these classes
- 35. Experiments
- 36. Experiments Out of reach with previous techniques
- 37. Experiments Performance improvement Almost 3hours with previous techniques
- 38. Scalability A A1 An A2 … e ⊙ e′  e = z1 ∧ z1 = z2 ∧ … ∧ zk−1 = zk ⊙ zk = e′  n k sec sec
- 39. General framework for DPNs with arithmetic Formal analysis paired with data abstraction techniques No ad-hoc algorithms: SMT as a Swiss Army knife Recent progress: CTL* model checking [IJCAR22] SMT for discovery, tight discovery-reasoning integration On- fi eld validation?