Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf ·...
Transcript of Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf ·...
![Page 1: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/1.jpg)
Assertions and Measurementsfor Mixed-Signal Simulation
PhD Thesis
Thomas Ferrere
VERIMAG, University of Grenoble (directeur: Oded Maler)Mentor Graphics Corporation (co-encadrant: Ernst Christen)
October 28, 2016
![Page 2: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/2.jpg)
Cyber-Physical SystemsI Both discrete and continuous modes of operation
I Example: a cell phone• A design:
• A bug:
(courtesy of Samsung and AppleInsider)
I Verification is needed1 / 40
![Page 3: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/3.jpg)
Cyber-Physical SystemsI Both discrete and continuous modes of operation
I Example: a cell phone• A design:
• A bug:
(courtesy of Samsung and AppleInsider)
I Verification is needed1 / 40
![Page 4: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/4.jpg)
Cyber-Physical SystemsI Both discrete and continuous modes of operation
I Example: a cell phone• A design:
• A bug:
(courtesy of Samsung and AppleInsider)
I Verification is needed1 / 40
![Page 5: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/5.jpg)
Cyber-Physical SystemsI Both discrete and continuous modes of operation
I Example: a cell phone• A design:
• A bug:
(courtesy of Samsung and AppleInsider)
I Verification is needed1 / 40
![Page 6: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/6.jpg)
Cyber-Physical SystemsI Both discrete and continuous modes of operation
I Example: a cell phone• A design:
• A bug:
(courtesy of Samsung and AppleInsider)
I Verification is needed1 / 40
![Page 7: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/7.jpg)
Mixed-Signal Simulation
Integrated Circuits
(courtesy of ST Microelectronics)
I Implement both analog anddigital electronics
I Design uses HDL and net lists atseveral stages
Modeling
I Digital: event-driven
q = 0 q = 1
↑ p
↑ p
I Analog: algebraic differentialequations
fp
(x,
dx
dt
)= 0
I Mixed-Signal: analog events↑(x > 2.0) and digital control fq
2 / 40
![Page 8: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/8.jpg)
Mixed-Signal Simulation
Integrated Circuits
(courtesy of ST Microelectronics)
I Implement both analog anddigital electronics
I Design uses HDL and net lists atseveral stages
Modeling
I Digital: event-driven
q = 0 q = 1
↑ p
↑ p
I Analog: algebraic differentialequations
fp
(x,
dx
dt
)= 0
I Mixed-Signal: analog events↑(x > 2.0) and digital control fq
2 / 40
![Page 9: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/9.jpg)
Simulation-Based Verification
I During the design stage run multiple simulationsI Each simulation produces a trace
• Records evolution of quantities over time• Real-valued and Boolean signals
I Monitoring: each traced need to be analysed• Evaluate requirements: correctness, robusteness, diagnostics• In general measuring some performance
I Automation of the monitoring activity:• Additional observer blocks• Declarative property or measurement languages
3 / 40
![Page 10: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/10.jpg)
Declarative Languages in Industry
Assertions
I Digital domainI Languages psl and sva built using two layers:
• regular expression• temporal logic
I Discrete time interpretation
Measurements
I Analog domain
I extract commands: signal processing, offline
I meas commands: event-driven, online
4 / 40
![Page 11: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/11.jpg)
Research on Realtime Properties
Problem: mixed-signal characterized by a synchronous interactionSolution: use continous-time representation
I Metric Temporal Logic (Koymans, 1990)• Signal Temporal Logic for real-valued signals (Maler and Nickovic,
2004)• Quantitative semantics for robustness estimate (Fainekos and Pappas,
2009)
I Timed Regular Expressions (Asarin, Caspi and Maler, 1998)
5 / 40
![Page 12: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/12.jpg)
Limitations of Existing Tools and Techniques
I Digital assertions bound to precision of sampling clock
I Realtime properties monitoring not implemented
I Robustness computation is not efficient
I No easy diagnostic of temporal logic properties failure
I Measurements not controllable by sequential conditions
I No analog measures in a digital context
6 / 40
![Page 13: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/13.jpg)
Outline
1. Preliminaries
2. Robustness Computation
3. Diagnostics
4. Regular Expressions Monitoring
5. Pattern-Based Measurements
6. Analog Measures in Digital Environment
7. Conclusion
7 / 40
![Page 14: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/14.jpg)
Outline
1. Preliminaries
2. Robustness Computation
3. Diagnostics
4. Regular Expressions Monitoring
5. Pattern-Based Measurements
6. Analog Measures in Digital Environment
7. Conclusion
7 / 40
![Page 15: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/15.jpg)
Signal Temporal Logic
I Propositions p: Boolean variables q, conditions x ≤ c, and events ↑ pI Temporal operators:
• Until: ϕUI ψ• Eventually: ♦I ψ = >UI ψ• Always: �I ψ = ¬♦I ¬ψ
Formulas can be written with ♦[a,b] and U only
I Example: stabilization property ϕ = �(↑ q → ♦[0,5]�[0,5] x ≤ 0.2)
t
x
t0 t0 + 5 t0 + 10
0.20
q
8 / 40
![Page 16: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/16.jpg)
Signal Temporal Logic
I Propositions p: Boolean variables q, conditions x ≤ c, and events ↑ pI Temporal operators:
• Until: ϕUI ψ• Eventually: ♦I ψ = >UI ψ• Always: �I ψ = ¬♦I ¬ψ
Formulas can be written with ♦[a,b] and U only
I Example: stabilization property ϕ = �(↑ q → ♦[0,5]�[0,5] x ≤ 0.2)
t
x
t0 t0 + 5 t0 + 10
0.20
q
8 / 40
![Page 17: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/17.jpg)
Monitoring
Offline approach (Maler and Nickovic, 2004): for each subformula ϕcompute set of times [ϕ]w where ϕ holds according to w
Definition (Satisfaction Set)
[p]w = {t : pw(t) = 1} [¬ϕ]w = [ϕ]w[♦[a,b] ϕ
]w = [ϕ]w [a, b] [ϕ ∨ ψ]w = [ϕ]w ∪ [ψ]w
9 / 40
![Page 18: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/18.jpg)
Computation
Theorem
For any ϕ and w with finite variability, [ϕ]w is finite union of intervals
I Eventually operator:
t
ϕ
♦[a,b] ϕ
T
T [a, b]
I Worst-case complexity O(|ϕ|)2 · |w|
10 / 40
![Page 19: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/19.jpg)
Example
t50
x
0.20
q
x ≤ 0.2
↑ q
�[0,5] x ≤ 0.2
♦[0,5]�[0,5] x ≤ 0.2
↑ q → ♦[0,5]�[0,5] x ≤ 0.2
�(↑ q → ♦[0,5]�[0,5] x ≤ 0.2)
11 / 40
![Page 20: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/20.jpg)
Example
t50
x
0.20
q
x ≤ 0.2
↑ q
�[0,5] x ≤ 0.2
♦[0,5]�[0,5] x ≤ 0.2
↑ q → ♦[0,5]�[0,5] x ≤ 0.2
�(↑ q → ♦[0,5]�[0,5] x ≤ 0.2)
11 / 40
![Page 21: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/21.jpg)
Example
t50
x
0.20
q
x ≤ 0.2
↑ q
�[0,5] x ≤ 0.2
♦[0,5]�[0,5] x ≤ 0.2
↑ q → ♦[0,5]�[0,5] x ≤ 0.2
�(↑ q → ♦[0,5]�[0,5] x ≤ 0.2)
11 / 40
![Page 22: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/22.jpg)
Example
t50
x
0.20
q
x ≤ 0.2
↑ q
�[0,5] x ≤ 0.2
♦[0,5]�[0,5] x ≤ 0.2
↑ q → ♦[0,5]�[0,5] x ≤ 0.2
�(↑ q → ♦[0,5]�[0,5] x ≤ 0.2)
11 / 40
![Page 23: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/23.jpg)
Example
t50
x
0.20
q
x ≤ 0.2
↑ q
�[0,5] x ≤ 0.2
♦[0,5]�[0,5] x ≤ 0.2
↑ q → ♦[0,5]�[0,5] x ≤ 0.2
�(↑ q → ♦[0,5]�[0,5] x ≤ 0.2)
11 / 40
![Page 24: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/24.jpg)
Example
t50
x
0.20
q
x ≤ 0.2
↑ q
�[0,5] x ≤ 0.2
♦[0,5]�[0,5] x ≤ 0.2
↑ q → ♦[0,5]�[0,5] x ≤ 0.2
�(↑ q → ♦[0,5]�[0,5] x ≤ 0.2)
11 / 40
![Page 25: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/25.jpg)
Example
t50
x
0.20
q
x ≤ 0.2
↑ q
�[0,5] x ≤ 0.2
♦[0,5]�[0,5] x ≤ 0.2
↑ q → ♦[0,5]�[0,5] x ≤ 0.2
�(↑ q → ♦[0,5]�[0,5] x ≤ 0.2)
11 / 40
![Page 26: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/26.jpg)
Quantitative Semantics
Robustness value JϕKw indicates how strongly ϕ is satisfied / violated by wI Positive if satisfied / negative if violated
I Magnitude = conservative estimate of distance to satisfaction /violation boundary
Definition (Robustness Signal)
Jx ≤ cKw = c− xw J¬ϕKw = − JϕKwq♦[a,b] ϕ
yw = t 7→ sup
t′∈[t+a,t+b]JϕKw (t′) Jϕ ∨ ψKw = max{JϕKw , JψKw}
12 / 40
![Page 27: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/27.jpg)
Outline
1. Preliminaries
2. Robustness Computation
3. Diagnostics
4. Regular Expressions Monitoring
5. Pattern-Based Measurements
6. Analog Measures in Digital Environment
7. Conclusion
12 / 40
![Page 28: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/28.jpg)
Principle
Theorem
For any ϕ and w piecewise linear, JϕKw is piecewise linear
I Until rewrite rules preserve the robustness value
I Timed eventually computed using optimal streaming algorithm of(Lemire, 2006) adapted to variable-step sampling
13 / 40
![Page 29: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/29.jpg)
Eventually Computation
I Problem: compute g(t) = supt′∈[t+a,t+b] f(t′)
I Solution: take maximum of f at t+ a, t+ b and sampling pointsinside (a, b)
f
t+ a t+ b
•i2
14 / 40
![Page 30: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/30.jpg)
Eventually Computation
I Problem: compute g(t) = supt′∈[t+a,t+b] f(t′)
I Solution: take maximum of f at t+ a, t+ b and sampling pointsinside (a, b)
f
t+ a t+ b
•i1
•i2
•i3
•i4
14 / 40
![Page 31: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/31.jpg)
Eventually Computation
I Problem: compute g(t) = supt′∈[t+a,t+b] f(t′)
I Solution: take maximum of f at t+ a, t+ b and sampling pointsinside (a, b)
f
t+ a t+ b
•i1
•i2
•i3
•i4
•i5
14 / 40
![Page 32: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/32.jpg)
Eventually Computation
I Problem: compute g(t) = supt′∈[t+a,t+b] f(t′)
I Solution: take maximum of f at t+ a, t+ b and sampling pointsinside (a, b)
f
t+ a t+ b
•i1
•i2
•i3 •
i5
14 / 40
![Page 33: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/33.jpg)
Eventually Computation
I Problem: compute g(t) = supt′∈[t+a,t+b] f(t′)
I Solution: take maximum of f at t+ a, t+ b and sampling pointsinside (a, b)
f
t+ a t+ b
•i1
•i2
•i5
14 / 40
![Page 34: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/34.jpg)
Eventually Computation
I Problem: compute g(t) = supt′∈[t+a,t+b] f(t′)
I Solution: take maximum of f at t+ a, t+ b and sampling pointsinside (a, b)
f
t+ a t+ b
•i1
•i2
•i5
14 / 40
![Page 35: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/35.jpg)
Eventually Computation
I Problem: compute g(t) = supt′∈[t+a,t+b] f(t′)
I Solution: take maximum of f at t+ a, t+ b and sampling pointsinside (a, b)
f
t+ a t+ b
•i2
•i5
14 / 40
![Page 36: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/36.jpg)
Example
t
x
0.2
x ≤ 0.2
0
�[0,5] x ≤ 0.2
0
♦[0,5]�[0,5] x ≤ 0.2
0
5015 / 40
![Page 37: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/37.jpg)
Evaluation
I Worst-case complexity in 2O(|ϕ|) · |w|I Implementation benchmarked with random signals:
|w| 102 103 104 105
♦[1,2] 0.0031 0.0030 0.0040 0.019♦[1,11] 0.0029 0.0026 0.0039 0.017♦[1,21] 0.0027 0.0026 0.0041 0.018♦[1,31] 0.0030 0.0028 0.0041 0.021
I Cost of computing ♦[a,b] independent from b− aI Improves on related works by several orders of magnitude
16 / 40
![Page 38: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/38.jpg)
Publications
I Donze, Ferrere, and Maler. Efficient robust monitoring for STL. InComputer Aided Verification (CAV), 2013.
16 / 40
![Page 39: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/39.jpg)
Outline
1. Preliminaries
2. Robustness Computation
3. Diagnostics
4. Regular Expressions Monitoring
5. Pattern-Based Measurements
6. Analog Measures in Digital Environment
7. Conclusion
16 / 40
![Page 40: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/40.jpg)
Motivation
I Find small segment of w sufficient to cause violation of ϕ
I Example: violation of �(↑ q → ♦[0,5]�[0,5] x ≤ 0.2)
t
x
0.20
q
50
I Sub-traces = temporal implicants
17 / 40
![Page 41: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/41.jpg)
Motivation
I Find small segment of w sufficient to cause violation of ϕ
I Example: violation of �(↑ q → ♦[0,5]�[0,5] x ≤ 0.2)
t
x
0.20
q
50
I Sub-traces = temporal implicants
17 / 40
![Page 42: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/42.jpg)
Propositional Implicants
I Implicant of ϕ ≈ partial valuation whose extensions satisfy ϕ
Definition
Implicant of ϕ = term γ such that γ ⇒ ϕPrime implicant of ϕ = implicant of ϕ maximal relative to ⇒
I For diagnostic: implicant compatible with observed values v
Problem (Diagnostic)
For given ϕ and v, find γ ⇒ ¬ϕ such that v |= γ
18 / 40
![Page 43: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/43.jpg)
Propositional Implicants
I Implicant of ϕ ≈ partial valuation whose extensions satisfy ϕ
Definition
Implicant of ϕ = term γ such that γ ⇒ ϕPrime implicant of ϕ = implicant of ϕ maximal relative to ⇒
I For diagnostic: implicant compatible with observed values v
Problem (Diagnostic)
For given ϕ and v, find γ ⇒ ¬ϕ such that v |= γ
18 / 40
![Page 44: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/44.jpg)
Temporal Implicants
I Temporal implicant of ϕ ≈ partial trace whose extensions satisfy ϕI Syntactical considerations:
• Terms with conjunctions∧
t∈T θ(t) over intervals• Limit values handled by non-standard reals t+, t−
I Example: ∧t∈[0.5,3.0]
¬p(t) ⇒ ¬♦[1,2] p
Theorem
Every realtime property ϕ has a prime implicant
Relies on boundedness of the time domain and non-standard extension
19 / 40
![Page 45: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/45.jpg)
Computation for Signal Temporal Logic
Diagnostic operators E, F such that:
I Explanation E(ϕ)⇒ ϕ
I Falsification F (ϕ)⇒ ¬ϕ
Definition (Diagnostic Signal)
E(p) = p E(¬ϕ) = F (ϕ)
E(♦[a,b] ϕ) = t 7→ E(ϕ)(ξ(t)) F (♦[a,b] ϕ) = t 7→∧
t′∈[t+a,t+b]
F (ϕ)(t′)
with selection function ξ such that ξ(t) ∈ [t+ a, t+ b]
20 / 40
![Page 46: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/46.jpg)
Selection FunctionCompute ξ over some interval T where ♦[a,b] ϕ holds:
I Current time t is at start of T
I Select last witness s of ϕ to account for ♦[a,b] ϕ at t
I Remove from T the part R that has been accounted for
ϕ
♦[a,b] ϕ
•t
already covered
T
21 / 40
![Page 47: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/47.jpg)
Selection FunctionCompute ξ over some interval T where ♦[a,b] ϕ holds:
I Current time t is at start of T
I Select last witness s of ϕ to account for ♦[a,b] ϕ at t
I Remove from T the part R that has been accounted for
ϕ
♦[a,b] ϕ
•t
already covered
T
[t+ a, t+ b]
21 / 40
![Page 48: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/48.jpg)
Selection FunctionCompute ξ over some interval T where ♦[a,b] ϕ holds:
I Current time t is at start of T
I Select last witness s of ϕ to account for ♦[a,b] ϕ at t
I Remove from T the part R that has been accounted for
ϕ
♦[a,b] ϕ
•t
•s
already covered
T
[t+ a, t+ b]
21 / 40
![Page 49: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/49.jpg)
Selection FunctionCompute ξ over some interval T where ♦[a,b] ϕ holds:
I Current time t is at start of T
I Select last witness s of ϕ to account for ♦[a,b] ϕ at t
I Remove from T the part R that has been accounted for
ϕ
♦[a,b] ϕ
•t
•s
already covered R
T
21 / 40
![Page 50: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/50.jpg)
Selection FunctionCompute ξ over some interval T where ♦[a,b] ϕ holds:
I Current time t is at start of T
I Select last witness s of ϕ to account for ♦[a,b] ϕ at t
I Remove from T the part R that has been accounted for
ϕ
♦[a,b] ϕ
•t
•s
already covered R
T
21 / 40
![Page 51: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/51.jpg)
OverviewI Example:
t0 5
x ≤ 0.2
↑ q
�[0,5] x ≤ 0.2
♦[0,5]�[0,5] x ≤ 0.2
↑ q → ♦[0,5]�[0,5] x ≤ 0.2
�(↑ q → ♦[0,5]�[0,5] x ≤ 0.2)
I Worst-case complexity O(|ϕ|)2 · |w|22 / 40
![Page 52: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/52.jpg)
OverviewI Example:
t0 5
x ≤ 0.2
↑ q
�[0,5] x ≤ 0.2
♦[0,5]�[0,5] x ≤ 0.2
↑ q → ♦[0,5]�[0,5] x ≤ 0.2
�(↑ q → ♦[0,5]�[0,5] x ≤ 0.2)
I Worst-case complexity O(|ϕ|)2 · |w|22 / 40
![Page 53: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/53.jpg)
OverviewI Example:
t0 5
x ≤ 0.2
↑ q
�[0,5] x ≤ 0.2
♦[0,5]�[0,5] x ≤ 0.2
↑ q → ♦[0,5]�[0,5] x ≤ 0.2
�(↑ q → ♦[0,5]�[0,5] x ≤ 0.2)
I Worst-case complexity O(|ϕ|)2 · |w|22 / 40
![Page 54: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/54.jpg)
OverviewI Example:
t0 5
x ≤ 0.2
↑ q
�[0,5] x ≤ 0.2
♦[0,5]�[0,5] x ≤ 0.2
↑ q → ♦[0,5]�[0,5] x ≤ 0.2
�(↑ q → ♦[0,5]�[0,5] x ≤ 0.2)
I Worst-case complexity O(|ϕ|)2 · |w|22 / 40
![Page 55: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/55.jpg)
OverviewI Example:
t0 5
x ≤ 0.2
↑ q
�[0,5] x ≤ 0.2
♦[0,5]�[0,5] x ≤ 0.2
↑ q → ♦[0,5]�[0,5] x ≤ 0.2
�(↑ q → ♦[0,5]�[0,5] x ≤ 0.2)
I Worst-case complexity O(|ϕ|)2 · |w|22 / 40
![Page 56: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/56.jpg)
OverviewI Example:
t0 5
x ≤ 0.2
↑ q
�[0,5] x ≤ 0.2
♦[0,5]�[0,5] x ≤ 0.2
↑ q → ♦[0,5]�[0,5] x ≤ 0.2
�(↑ q → ♦[0,5]�[0,5] x ≤ 0.2)
I Worst-case complexity O(|ϕ|)2 · |w|22 / 40
![Page 57: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/57.jpg)
Publications
I Ferrere, Maler, and Nickovic. Trace diagnostics using temporalimplicants. In Automated Technology for Verification and Analysis(ATVA), 2015.
22 / 40
![Page 58: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/58.jpg)
Outline
1. Preliminaries
2. Robustness Computation
3. Diagnostics
4. Regular Expressions Monitoring
5. Pattern-Based Measurements
6. Analog Measures in Digital Environment
7. Conclusion
22 / 40
![Page 59: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/59.jpg)
Signal Regular Expressions
I Propositions p: Boolean variables q, threshold conditions x ≤ cI Atomic expressions: holding p, events ↑ pI Concatenation: ϕ · ψI Kleene star: ϕ∗
I Duration restriction: 〈ϕ〉I
23 / 40
![Page 60: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/60.jpg)
ExamplePulse pattern: ψ = ↓ r · 〈q · p · q〉[5,6] · ↑ r
q p q ↑ r↓ rt
x
7.0
4.0
∈ [5, 6]
p = (x ≤ 4.0)
q = (4.0 < x ≤ 7.0)
r = (x > 7.0)
24 / 40
![Page 61: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/61.jpg)
Monitoring
I For any w expression ϕ defines a set of segments (t, t′) such thatw[t, t′] matches ϕ
I Offline approach: for all subexpressions ϕ compute the complete setof matches [ϕ]w of ϕ relative to w
Definition (Match Set)
[p]
w = {(t, t′) : t < t′′ < t′ → pw(t′′) = 1} [ϕ ∨ ψ]w = [ϕ]w ∪ [ψ]w
[〈ϕ〉I ]w = {(t, t′) : t′ − t ∈ I} ∩ [ϕ]w [ϕ ∧ ψ]w = [ϕ]w ∩ [ψ]w
[ϕ · ψ]w = [ϕ]w # [ψ]w [ϕ∗]w =⋃i≥0
[ϕi]
w
25 / 40
![Page 62: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/62.jpg)
Match Set Representation
I A zone = convex set with horizontal, vertical and diagonal boundaries
I Represents a set of signal segments
t
t′
Theorem
For any ϕ and w with finite variability, [ϕ]w is a finite union of zones
26 / 40
![Page 63: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/63.jpg)
Match Set RepresentationI A zone = convex set with horizontal, vertical and diagonal boundariesI Represents a set of signal segments
t, t′
t
t′
p
Theorem
For any ϕ and w with finite variability, [ϕ]w is a finite union of zones
26 / 40
![Page 64: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/64.jpg)
Match Set RepresentationI A zone = convex set with horizontal, vertical and diagonal boundariesI Represents a set of signal segments
t, t′
t
t′
p
s
•
s′
Theorem
For any ϕ and w with finite variability, [ϕ]w is a finite union of zones
26 / 40
![Page 65: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/65.jpg)
Match Set RepresentationI A zone = convex set with horizontal, vertical and diagonal boundariesI Represents a set of signal segments
t, t′
t
t′
p
s
•
s′
Theorem
For any ϕ and w with finite variability, [ϕ]w is a finite union of zones
26 / 40
![Page 66: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/66.jpg)
Example
〈p〉[2,4] · 〈q〉[1,2]
I Match set of p
I Match set of 〈p〉[2,4]
I Match set of 〈q〉[1,2]
I Match set of 〈p〉[2,4] · 〈q〉[1,2]
t, t′
t
t′
p
q
27 / 40
![Page 67: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/67.jpg)
Example
〈p〉[2,4] · 〈q〉[1,2]
I Match set of p
I Match set of 〈p〉[2,4]
I Match set of 〈q〉[1,2]
I Match set of 〈p〉[2,4] · 〈q〉[1,2]
t, t′
t
t′
p
q
27 / 40
![Page 68: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/68.jpg)
Example
〈p〉[2,4] · 〈q〉[1,2]
I Match set of p
I Match set of 〈p〉[2,4]
I Match set of 〈q〉[1,2]
I Match set of 〈p〉[2,4] · 〈q〉[1,2]
t, t′
t
t′
s
•
s′
p
q
27 / 40
![Page 69: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/69.jpg)
Example
〈p〉[2,4] · 〈q〉[1,2]
I Match set of p
I Match set of 〈p〉[2,4]
I Match set of 〈q〉[1,2]
I Match set of 〈p〉[2,4] · 〈q〉[1,2]
t, t′
t
t′
p
q
27 / 40
![Page 70: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/70.jpg)
Example
〈p〉[2,4] · 〈q〉[1,2]
I Match set of p
I Match set of 〈p〉[2,4]
I Match set of 〈q〉[1,2]
I Match set of 〈p〉[2,4] · 〈q〉[1,2]
t, t′
t
t′
p
q
27 / 40
![Page 71: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/71.jpg)
Example
〈p〉[2,4] · 〈q〉[1,2]
I Match set of p
I Match set of 〈p〉[2,4]
I Match set of 〈q〉[1,2]
I Match set of 〈p〉[2,4] · 〈q〉[1,2]
t, t′
t
t′
p
q
27 / 40
![Page 72: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/72.jpg)
Example
〈p〉[2,4] · 〈q〉[1,2]
I Match set of p
I Match set of 〈p〉[2,4]
I Match set of 〈q〉[1,2]
I Match set of 〈p〉[2,4] · 〈q〉[1,2]
t, t′
t
t′
p
q
27 / 40
![Page 73: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/73.jpg)
Example
〈p〉[2,4] · 〈q〉[1,2]
I Match set of p
I Match set of 〈p〉[2,4]
I Match set of 〈q〉[1,2]
I Match set of 〈p〉[2,4] · 〈q〉[1,2]
t, t′
t
t′
p
q
27 / 40
![Page 74: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/74.jpg)
Example
〈p〉[2,4] · 〈q〉[1,2]
I Match set of p
I Match set of 〈p〉[2,4]
I Match set of 〈q〉[1,2]
I Match set of 〈p〉[2,4] · 〈q〉[1,2]
t, t′
t
t′
p
q
s
•
••
s′′ s′
27 / 40
![Page 75: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/75.jpg)
Kleene Star
On bounded traces w the sequence∨ni=0 ϕ
i converges to a fix-point infinitely many steps
I Assume w can be split in m constant segments v of length less that 1
I Over each segment either [ϕ]v = [>]v or [ϕ]v = [⊥]v
Lemma
[ϕn]w ⊆[ϕn−1
]w for any n > 2m+ 1
Compute∨ni=0 ϕ
i by squaring: ε, ϕ, ϕ2, ϕ4, . . ., ϕ2k up tok > log(2m+ 1)
28 / 40
![Page 76: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/76.jpg)
Evaluation
I Worst-case complexity: |w|O(|ϕ|) without star
I Implementation using DBM for efficient zones computation
I Benchmarked for
ϕ = 〈(〈p · ¬p〉[0,10])∗ ∧ (〈q · ¬q〉[0,10])∗〉[80,∞]
with randomized traces:
|w| |[ϕ]w| time3654 0 0.276715 10 1.35
13306 23 2.7326652 47 5.83
I Observed performance linear in |w|
29 / 40
![Page 77: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/77.jpg)
Publications
I Ulus, Ferrere, Asarin, and Maler. Timed pattern matching. In FormalModeling and Analysis of Timed Systems (FORMATS), 2014.
I Ulus, Ferrere, Asarin, and Maler. Online timed pattern matching usingderivatives In Tools and Algorithms for the Construction and Analysisof Systems (TACAS), 2016.
29 / 40
![Page 78: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/78.jpg)
Outline
1. Preliminaries
2. Robustness Computation
3. Diagnostics
4. Regular Expressions Monitoring
5. Pattern-Based Measurements
6. Analog Measures in Digital Environment
7. Conclusion
29 / 40
![Page 79: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/79.jpg)
Measurement Language
I Motivation: automate the extraction of mixed-signal measures
I Signal Regular Expressions control when the measure takes place
I Measure: aggregating operator duration, min, max, and average
I Example:
average(↑(x > 1.0) · (x > 1.0) · ↓(x > 1.0))
measures average value of x on high portions
30 / 40
![Page 80: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/80.jpg)
Conditionals and Events
Construct expressions delimited by events
I conditional operators:• ?ϕ begins a match of ϕ• !ϕ ends a match of ϕ
I event-bounded expressions ψ:• event ↑ p, ↓ p• conditional event ψ?, ψ!• sequence ψ · ϕ · ψ
Theorem
For any w and ψ event-bounded, [ϕ]ψ is finite
31 / 40
![Page 81: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/81.jpg)
Case Study: Distributed System Interface
I DSI3 is a protocol for electronics in automotive industry
I Based on pulse communication
I Requirements about magnitude of signals and timing of events
I Implementation: behavioral model
e(t) a(t)
R
C
Controler Sensor
i
v
32 / 40
![Page 82: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/82.jpg)
Timing Requirement
q p q
rψ ψ
↑ r↓ r
ψ?
t
x
7.0
4.0
∈ [5, 6]
time between consecutive pulses
33 / 40
![Page 83: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/83.jpg)
Results
I Pulse description:
ψ = ↓ r · 〈q · p · q〉[5,6] · ↑ r
I Measure expression:
ϕ = duration(ψ · r · ψ?)
I Computation time cost:
|w| quantize match extract total
1 · 106 0.047 0.617 0.000 0.6645 · 106 0.197 0.612 0.000 0.8091 · 107 0.386 0.606 0.000 0.9922 · 107 0.759 0.609 0.000 1.368
34 / 40
![Page 84: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/84.jpg)
Publications
I Ferrere, Maler, Nickovic, and Ulus. Measuring with timed patterns. InComputer Aided Verification (CAV), 2015.
34 / 40
![Page 85: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/85.jpg)
Outline
1. Preliminaries
2. Robustness Computation
3. Diagnostics
4. Regular Expressions Monitoring
5. Pattern-Based Measurements
6. Analog Measures in Digital Environment
7. Conclusion
34 / 40
![Page 86: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/86.jpg)
Analog Measurements and Digital Testbench
I Simulator-implemented measures provide guarantees:• accuracy• reproducible
I Unfortunately only accessible in analog environmentI Digital testbench enables structured verification
• assertion tracking• coverage indicators• . . .
I Mixed-signal verification often done with user-defined monitors
35 / 40
![Page 87: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/87.jpg)
Measurement Tasks
I We propose new measurements functions as system tasks
taskµ(x, p, y, q, e, r)
I Input: (x, p), output: (y, q)
I Control: enable event e and reset event r
I Accessed in a variety of context: module, class, etc.
I Prototype implementation using VPI with functions: initializeµ,updateµ, statusµ, and evaluateµ
36 / 40
![Page 88: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/88.jpg)
Phase Locked Loop
I Digital testbench using the Universal Verification Methodology:
I Measure relative jitter online, locking time and enforce safe operatingarea of current through VDD
I Computation time < 1s for measurements, ≈ 300s for simulation
37 / 40
![Page 89: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/89.jpg)
Outline
1. Preliminaries
2. Robustness Computation
3. Diagnostics
4. Regular Expressions Monitoring
5. Pattern-Based Measurements
6. Analog Measures in Digital Environment
7. Conclusion
37 / 40
![Page 90: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/90.jpg)
Contributions
I Diagnostic procedure for realtime assertions
I Efficient algorithms for robustness computation
I Monitoring of regular expressions
I Pattern-based measurements
I Bring practice of analog and digital verification closer
38 / 40
![Page 91: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/91.jpg)
Publications
1. Donze, Ferrere, and Maler. Efficient robust monitoring for STL. InComputer Aided Verification (CAV), 2013.
2. Ulus, Ferrere, Asarin, and Maler. Timed pattern matching. In FormalModeling and Analysis of Timed Systems (FORMATS), 2014.
3. Ferrere, Maler, Nickovic, and Ulus. Measuring with timed patterns. InComputer Aided Verification (CAV), 2015.
4. Ferrere, Maler, and Nickovic. Trace diagnostics using temporalimplicants. In Automated Technology for Verification and Analysis(ATVA), 2015.
5. Ulus, Ferrere, Asarin, and Maler. Online timed pattern matching usingderivatives In Tools and Algorithms for the Construction and Analysisof Systems (TACAS), 2016.
39 / 40
![Page 92: Assertions and Measurements for Mixed-Signal Simulation ...maler/Papers/slides-thesis-thomas.pdf · Assertions and Measurements for Mixed-Signal Simulation PhD Thesis Thomas Ferr](https://reader034.fdocuments.net/reader034/viewer/2022043005/5f8cebc9309aaf46a6378a69/html5/thumbnails/92.jpg)
Future Works
I Robustness of Signal Regular Expressions
I New monitoring algorithms for SRE
I Integrate SRE with STL
I Formal verification using regular expressions
40 / 40