paretolib: a python library for parameter synthesis · faster convergence than pre-dating similar...
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Bâtiment IMAG, Université Grenoble Alpes700, avenue centrale
38401 Saint Martin d’Hères, Francehttp://www-verimag.imag.fr
ParetoLib: A Python Library for Parameter
SynthesisJosé-Ignacio Requeno
Alexey BakhirkinNicolas Basset
Oded Maler*
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CONTEXT
Context
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CYBER-PHYSICAL SYSTEMS
© Antoine Heusse
■ Cyber-Physical Systems:► hardware/software interacting with the physical environment► computerized control systems► uncertain / changing environment (timing constraints)► large scale, distributed / networked
■ Criticality:► safety (absence of errors)► security (resistance to attacks)► certification
■ Validation & Verification:► hybrid: discrete + real-time systems
+
© Sancio83
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MONITORING
► Models are generally hybrid systems producing hybrid traces► Runtime verification (aka monitoring) analyses a single behavior at a
time
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MONITORING
► Models are generally hybrid systems producing hybrid traces► Runtime verification (aka monitoring) analyses a single behavior at a
time
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MOTIVATION
After 2s, the signal is never above 3
*Donzé, A.: On signal temporal logic. In: Legay, A., Bensalem, S. (eds.) RV 2013. LNCS, vol. 8174, pp. 382–383. Springer, Heidelberg (2013).
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STL EXAMPLE
After 2s, the signal is never above 3
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PROBLEM
Parameter Synthesis
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PARAMETER SYNTHESIS
Given a Parametric STL formula
𝝋𝝋(𝒑𝒑𝟏𝟏, … ,𝒑𝒑𝒏𝒏)
identify the valuations 𝒗𝒗(𝒑𝒑𝒊𝒊) such that
𝒙𝒙 ⊨ 𝝋𝝋(𝒗𝒗(𝒑𝒑𝟏𝟏), … ,𝒗𝒗(𝒑𝒑𝒏𝒏))
for each parameter 𝒑𝒑𝒊𝒊
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SIGNAL STABILIZATION
Always |x| > _ then after _ s, |x| settles under _ for _ s
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SIGNAL STABILIZATION
Always |x| > _ then after _ s, |x| settles under _ for _ s
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PARAMETER SYNTHESIS
■ Challenges► Multiple solutions: which one to chose?► Tightness implies to “optimize” the valuation 𝑣𝑣(𝑝𝑝𝑖𝑖) for each parameter 𝑝𝑝𝑖𝑖
■ The multi-criteria optimization problem can be greatly simplified if the formula is monotonic in each 𝒑𝒑𝒊𝒊► In case of monoticity, the border of the validity domain has the
structure of a Pareto front
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VALIDITY DOMAINS
► The validity domain 𝑿𝑿 of formula 𝝋𝝋 and signal 𝒙𝒙 is the set of valuations𝒗𝒗(𝒑𝒑𝒊𝒊) such that 𝒙𝒙 ⊨ 𝝋𝝋(𝒗𝒗(𝒑𝒑𝟏𝟏), … ,𝒗𝒗(𝒑𝒑𝒏𝒏)) for each parameter 𝒑𝒑𝒊𝒊
► In case of monoticity, the border of the validity domain has the structure of a Pareto front
𝑝𝑝1
𝑝𝑝2
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SIGNAL STABILIZATION
Always |x| > 0.5 then after 1s, |x| settles under 0.5 for 1.5 s
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PARETOLIB
ParetoLib
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PARETOLIB
■ Python library for solving multi-criteria optimization problems:► Faster convergence than pre-dating similar algorithms► Parallel computation in multi-core CPU’s► Generic interface for domain-specific decision procedures (Oracle)
■ Application to parameter synthesis:► Integration with Signal Temporal Logic runtime monitors► Experiments with parametric Signal Temporal Logic specifications
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PARETOLIB LIBRARY
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PARETOLIB LIBRARY
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PARETOLIB LIBRARY
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PARETOLIB LIBRARY
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PARETOLIB LIBRARY
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PARETOLIB LIBRARY
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PARETOLIB LIBRARY
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PARETOLIB LIBRARY
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PARETOLIB LIBRARY
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EXPERIMENTS
Experiments
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EXPERIMENTS
Always |x| > _ then after _ s, |x| settles under _ for _ s
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EXPERIMENTS
Always |x| > _ then after _ s, |x| settles under _ for _ s
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EXPERIMENTS
Always |x| > p2 then after p1 s, |x| settles under p2 indefinitely
𝜑𝜑 ≔ F 0,𝑝𝑝1 G 0,∞ (On 0,∞ Max 𝑥𝑥 − On 0,∞ Min 𝑥𝑥)) < 𝑝𝑝2
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EXPERIMENTS
Always |x| > p2 then after p1 s, |x| settles under p2 indefinitely
𝜑𝜑 ≔ F 0,𝑝𝑝1 G 0,∞ (On 0,∞ Max 𝑥𝑥 − On 0,∞ Min 𝑥𝑥)) < 𝑝𝑝2
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EXPERIMENTS
Always |x| > 0.25 then after 155 s, |x| settles under 0.25 indefinitely
𝜑𝜑 ≔ F 0,155 G 0,∞ (On 0,∞ Max 𝑥𝑥 − On 0,∞ Min 𝑥𝑥)) < 0.25
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EXPERIMENTS
Always |x| > 0.25 then after 155 s, |x| settles under 0.25 indefinitely
𝜑𝜑 ≔ F 0,155 G 0,∞ (On 0,∞ Max 𝑥𝑥 − On 0,∞ Min 𝑥𝑥)) < 0.25
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CONCLUSIONS
Conclusions
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CONCLUSIONS
■ Python library for solving multi-criteria optimization problems:► Faster convergence than pre-dating similar algorithms► Parallel computation in multi-core CPU’s► Generic interface for domain-specific decision procedures (Oracle)
■ Application to parameter synthesis:► Integration with Signal Temporal Logic runtime monitors► Experiments with parametric Signal Temporal Logic specifications
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FUTURE WORK
■ Python library for solving multi-criteria optimization problems:► Keep on improving the tool performance► Introduction of new features
■ Application to parameter synthesis:► Integration with new temporal logics
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THE END