Maximal and minimal dynamic Petri net slicing

What is it about?

This paper is about Petri net slicing, a technique to reduce the size of a Petri net to ease the analysis or understanding of the original Petri net. The paper presents two new Petri net slicing algorithms to isolate those places and transitions of a Petri net (the slice) that may contribute tokens to one or more places given (the slicing criterion). The two algorithms proposed are formalized. The maximality of the first algorithm and the minimality of the second algorithm are formally proven. Both algorithms, together with three other state-of-the-art algorithms, have been implemented and integrated into a single tool so that we have been able to carry out a fair empirical evaluation. Besides the two new Petri net slicing algorithms, a public, free, and open-source implementation of five algorithms is reported. The results of an empirical evaluation of the new algorithms and the slices they produce are also presented. The first algorithm collects all places and transitions that may contribute tokens (in any computation) to the slicing criterion. In contrast, the second algorithm collects the places and transitions needed to fire the shortest transition sequence that contributes tokens to some place in the slicing criterion. Therefore, the net computed by the first algorithm can reproduce any computation that contributes tokens to any place of interest. In contrast, the second algorithm loses this possibility, but it often produces a much more reduced subnet (which still can reproduce some computations that contribute tokens to some places of interest). The first algorithm is proven maximal, and the second one is proven minimal.

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Photo by Joshua Rawson-Harris on Unsplash

Photo by Joshua Rawson-Harris on Unsplash

Why is it important?

This paper provides a theoretical basis to reason about Petri net slicing formally. Moreover, the algorithms proposed are proven maximal and minimal. These are the first Petri net slicing algorithms proven minimal and maximal, so there does not exist another Petri net algorithm that can produce more accurate slices.