Introduction
-
We innovatively integrate environment models with system properties, which are accurately represented and translated into monitor form by modeling and quantitatively analyzing the environment.
-
By optimizing the monitor insertion algorithm, we succeeded in significantly reducing the average execution time of the monitor, which is only 41.1\(\%\) of the pre-optimization execution time.
Background
Linear temporal logic
-
Gp: p must be true throughout the timeline
-
Fp: p must be true at some point in the present or future
-
Xp: p must be true at the next time point
-
pUq: q is true at present, or q becomes true at some point in the future before p stops being true
Büchi Automaton
-
Q is a finite nonempty set of states,
-
\(Q_0 \subseteq Q\) is a set of initial states,
-
\(\Pi : \Pi =2^{A P}\) is the input alphabet (set of atomic propositions),
-
\(\sigma : \sigma \subseteq Q \times \Pi \times Q\) is nondeterministic transfer relationship,
-
\(F: F \subseteq Q\) is a set of accepting states.
Runtime verification
Related work
Context-aware environmental modeling method
System framework
-
How to model and quantitatively analyze the system’s operating environment.
-
How to accurately characterize and describe the task properties of the system.
-
How to design an algorithm that combines two automata to generate a monitor.
Environment modeling
Category | Description |
---|---|
loc | Information about specific physical positions, such as location data from GPS sensors and the distances measured between two sensors. |
tab | Information are identified by sensors, such as temperature and facial recognition. |
time | Information about time-related features, such as request time and data read from a clock. |
behavior | Information about actions obtained from sensors, such as action information and door opening and closing. |
-
D : Set of states.
-
\(D_0:\) Initial state.
-
T : State transition function \(D \times T \rightarrow D\).
-
\(\Pi :\) Input alphabet, where \(\Pi =2^{A P}\).
-
\(\delta :\) Labeled probabilistic transition function \(Q\times \Pi \times Q \rightarrow [0,1]\).
-
\(\mu _0:\) Probability distribution over \(D_0\).
Classification | Description | Recommendation |
---|---|---|
Level 1 | Sunny: visibility greater than 10km, wind force less than level 4 | Observe the city traffic speed limit |
Level 2 | Cloudy: small amount of standing water | Do not exceed 50km/hour |
Level 3 | Light rain or snow: obvious standing water | Do not exceed 40km/hour |
Level 4 | Moderate rain or snow: blurry vision, easy to slip | Do not exceed 30km/hour |
Level 5 | Heavy rain or snow: covered with water or snow, poor visibility | Do not exceed 20km/hour |
Task formalization description
-
If property \(\varphi\) can be proven on the current observed finite path u, there is no need to consider future events, and the output is true.
-
If property \(\varphi\) can be proven on the current observed finite path u that it will not hold on any subsequent path, the output is false.
-
If it is impossible to prove whether property \(\varphi\) holds on the current observed finite path u, the output is inconclusive, and continuous monitoring is necessary in the future.
Monitor generation
Algorithm for generating monitors
LTL to AA
-
S is the set of states,
-
\(\Sigma\) represents an alphabet,
-
\(I\subseteq P_f(S)\)represents the initial state(s), and \(P_f(events)\) represents events that can occur simultaneously,
-
\(F\subseteq S\) represents a set of accepting states,
-
\(\delta : S \rightarrow P_f\left( P_f(S \times \Sigma )\right)\) represents a transition function.
AA to GBA
GBA to BA
The integrated algorithm for synthesizing the environment model and Büchi automaton
-
\(Q^\xi\) is the set of states,
-
\(Q_{0}^{\xi } : Q_{0}^{\xi } = \left( Q_0, D_0\right) \in Q^\xi\) is the set of initial states,
-
\(\Pi : \Pi =2^{A P}\) is the input alphabet (set of atomic propositions),
-
\(\delta :\) \(Q\times \Pi \times Q \rightarrow [0,1]\)is the labeled probabilistic transition function
-
\(\sigma = \sigma \times D \times T\) represents the transition relationship,
-
F is the set of accepting states.
-
\(\mu _0\) is the probability distribution over \(Q_{0}^{\xi }\)
Insertion process
Evaluation
Simulation experiment
Environmental parameters | Monitor | Simulation result |
---|---|---|
Index 1, Friction Coefficient 0.65 | \(\checkmark\) | Maintain Distance |
Index 1, Friction Coefficient 0.65 | \(\times\) | Maintain Distance |
Index 3, Friction Coefficient 0.41 | \(\checkmark\) | Maintain Distance |
Index 3, Friction Coefficient 0.41 | \(\times\) | Less than Safety Distance |
Index 5, Friction Coefficient 0.3 | \(\checkmark\) | Maintain Distance |
Index 5, Friction Coefficient 0.3 | \(\times\) | Collision Occurs |