Abstract
When formalising the quality dimensions in the previous chapter, we already slightly touched upon the difficulties that exist in quantifying process behaviour.
Some infinities are bigger than other infinities.
John Green
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Notes
- 1.
While the algorithm introduced in this chapter is used in the experiments of subsequent chapters, non-technical readers can skip this chapter without any harm to the continuity.
- 2.
This is so for the process tree notation. One could argue whether the third element is in fact part of the loop when considering other notations, but the point remains that it is always possible to transform a structured finite loop to a three-block construct.
- 3.
Note that when only a single of the children is executed—i.e. S only contains one path dictionary—then \(R = Parallel(S) = S\) according to Algorithm 3.3.
- 4.
\(\mathbb {P}(\{T_i\})\) refers to the set of all subsets of \(\{T_1, ..., T_u\}\).
- 5.
At least one of the branches of a non-exclusive choice should be executed.
- 6.
For the sake of completeness, there would be 8 different paths in the tree if we could observe silent transitions and distinguish the duplicate tasks from each other. When we label the leaf nodes in \(PT_4\) as \(a_1, \tau _1, a_2\) and \(\tau _2\), the tree can produce the following sequences: \(\langle a_1 a_2\rangle , \langle a_2 a_1\rangle ,\langle \tau _1 \tau _2\rangle , \langle \tau _2 \tau _1\rangle ,\langle a_1 \tau _2\rangle ,\langle a_2 \tau _1\rangle , \langle \tau _1 a_2\rangle , \langle \tau _2 a_1\rangle \).
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Janssenswillen, G. (2021). Calculating the Number of Distinct Paths in a Block-Structured Model. In: Unearthing the Real Process Behind the Event Data. Lecture Notes in Business Information Processing, vol 412. Springer, Cham. https://doi.org/10.1007/978-3-030-70733-0_3
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DOI: https://doi.org/10.1007/978-3-030-70733-0_3
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