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We exploit the system structure captured in the verifier net to guide the search for the desired new labeling function.
We formulate an integer linear programming problem that finds an optimal labeling function when numerical costs are associated with transition relabeling.
Starting from a non-diagnosable labeled Petri net system, we present a systematic procedure to design a new labeling function that makes the system diagnosable and optimizes a given objective function.
Thus, ϕ is a labeling function.
Then ϕ is a proper labeling function.
Proof First we show that ϕ is a labeling function.
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The main idea behind this method is to introduce phase field labeling functions in order to model the contact line by smooth change from one type of material to another.
The two observation functions obs1 and obs2 are characterized by labeling functions, say l1 and l2, respectively.
From the measurable structure of the problem, it turns out that we have to work with local, measurable labeling functions.
We encoded linear and non-linear labeling functions into the relevant variables.
On this dataset our method clearly outperformed rank correlation coefficients and indeed it is known that the latter method is sensitive to non-linear labeling functions (Fig. 2B middle).
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