- Computing Reviews, Aug. 2004, Vol.45(8), p.496
- Clustering for Petri Nets. Keller W. Theoretical Computer Science 308 (1-3): 145-197, 2003. Type: Article
- Reviewer: Richard Botting
This research paper is unusually baffling. First, it uses category theory. Second, it has occasional lapses in English. Third, it has a few small typographical errors in the mathematics (for example, (BM) instead of (B M) in Definition 2.5). Only people who have mastered the first 100 pages of Mac Lane’s classic [1] can be expected to understand it.
A theory is presented from the author’s Ph.D. dissertation [2]. Specifically, it offers a new theory of composing and decomposing Petri nets. The theory unifies clustering practice with folding theory. The key invention here is the category of one-sets. This is a subcategory of multi-sets, with fewer morphisms. Useful constructions like push-outs exist in it. The author proposes a new category of Petri net (PPNET) based on this, and then develops nine more. The author also proves relevant connections between them: coreflections, adjunctions, and functors. Specialists in the area will find the paper worth studying.
As stated above, this paper will interest researchers working on Petri nets. Sadly, Petri nets play a small role in software development. They appear in the unified modeling language, but there is little need for them to be composed or decomposed in practice. Practitioners can ignore this paper, however, the rest of the author’s dissertation may be of interest.
- Mac Lane, S. Categories for the working mathematician: Graduate Texts in Mathematics #5. Springer. 1971.
- Keller, W. Petri nets for reverse engineering. http://home.tiscalinet.ch/wkeller.