Abstract
Carl Adam Petri wrote his famous thesis over 50 years ago. In another 50 years will a future generation of scientists and practitioners look back on a hundred years of Petri nets? If so, what will they expose as the historic landmarks in their writing on Petri nets, and will these be the same as those the community has considered for the last 50 years?
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Notes
- 1.
Nearly 4000 citations (Google Scholar).
- 2.
Albeit sometimes only grudgingly: see the experimental results on teleportation, only a couple of years ago, and reactions in the literature confirming the misnamed ‘spooky action at a distance’.
- 3.
Anatol Holt’s role includes many contributions. He also coined the term ‘Petri nets’, according to a letter Petri sent to Holt, as reported in a memorial lecture for Petri.
- 4.
May 10, 2017.
- 5.
Often with a warning by the computer pioneer to make sure temporal assumptions are consistent with concurrency axioms: “This is only for convenience and ease of understanding in classical terms”; “Continuous real-time is based on the erroneous assumption of density, which contradicts our axioms in terms of measurement”; “Two integer clocks can be compared to arbitrary rational precision and ultimately violate either spatial density bounds for information or speed bounds for synchronisation when the machine keeps getting extended”.
- 6.
The original German terms ‘Stelle’ and ‘Stelligkeit’ also mean ‘position’ and ‘arity’ for token distribution variables in transitions or the entire net as functions on such distribution vectors.
- 7.
Dedekind cuts at the event occurrence net level, i.e. in terms of elementary firings and marking.
- 8.
Well before I studied there and met him while working as a student and later researcher at the GMD Schloß Birlinghoven, St. Augustin, near Bonn, where he was the foundation director of the Institute for Information Systems Theory (1968) later renamed to Methods Foundations, while I was conducting research in the neighbouring Institute for Systems Technology working on compiler construction from 1976 and later on software theory, the Segras specification language and a toolkit bridging algebraic-categorical specification and Petri nets.
- 9.
Course given by Klaus Berkling who later built the GMD reduction machine for his variant of the λ-calculus.
- 10.
Logical positivism: Only statements that are empirically verifiable are empirically meaningful. But how can we even set a test and verify without prior theory and meaning?
- 11.
Taught in Bonn, where, to my delight, his entire collected works was held in multiple copies.
- 12.
Only to be admitted to his defence on June 20, 1962, almost a year later.
- 13.
Fifty years before Germany would become the country with the fastest-growing Jewish population outside Israel.
- 14.
Through art, shared Yoga interest and hobbies such as bee keeping and, not least, Math tutoring of her children and endless fascinating table conversations and occasional short courses on Eastern philosophy and Hermetic literature.
- 15.
Who goes back to Hegel, not shown in the graph.
- 16.
Many students started a professional career during their last year of study or earlier. The average number of semesters was therefore 12 or more in this unregulated environment, due to part-time study in advanced years.
- 17.
From memory, 1979, due to Petri’s close links with MIT; I could make it crash occasionally by fast mouse movements; it was usable, and entirely written in Flavors, the object-oriented East Coast Lisp, which I would use later for both compiler construction and algebraic Petri net specification, and as a target for pilot implementations.
- 18.
This is out of the scope of this work. We refer to work by Valk, Smith, and Petri himself.
- 19.
As celebrated for instance by Mary Shaw’s and David Garlan’s articles, or speeches on software architecture practice and research at the International Conference on Software Engineering (2000 and beyond), the flagship conference of the software engineering discipline.
- 20.
https://www.microsoft.com/en-us/research/publication/arbiter-free-synchronization/ accessed mid-May 2017.
- 21.
Distinguishing evidence, affordance and allowance of harmful or unsafe behaviour.
- 22.
Several of us went on to study mathematics, not least due to Dr. Bosbach and his group theory workshops.
- 23.
Except for smoking without hesitation and without interruption, which was not uncommon in those days.
- 24.
I had carried them to the USA and Australia in long-distance moves and finally replaced most with their digital version, creating wiggle room in my study for other parallel interests.
- 25.
Including why I was holding on to them.
- 26.
https://www.rd-alliance.org/, of which I am a member.
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Acknowledgements
Writing this essay and chapter allowed me to go through a small collection of ‘gem’Footnote 24 papers and notes and really question hard what the longer-lasting issues were.Footnote 25 I used data analytics methods and results that would not have been possible without open science repositories such as the Mathematics/Ph.D. Genealogy project cited, the Research Data Alliance project for global research transparency,Footnote 26 Wikipedia science resources, and tools in eResearch at RMIT, where one of my roles is that of eResearch (eScience) director. This is gratefully acknowledged. This writing also allowed me to revive long-forgotten memories that otherwise would not have come to the fore—some shared here. More importantly and publicly, I owe deep thanks to the people I mentioned here or cited, notably Petri and his inner circle, and to many more there was no space or focus to mention, including close family and friends, whose journey was interwoven with the work and the times I write about. Their influence, especially in the early years of my study and career, should not be underestimated. What we are or become includes a fair measure of those around us, willing to share kindly and give forward, and willingness to accept, give back or pass on. I would also like to thank Marie-Luise Christ-Neumann and Jürgen Christoffel for keeping and sharing mementos of our former project at the GMD Bonn, and Alice Schopp, who reconnected me with Bruno Bosbach.
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Schmidt, H.W. (2019). Petri Nets: The Next 50 Years—An Invitation and Interpretative Translation. In: Reisig, W., Rozenberg, G. (eds) Carl Adam Petri: Ideas, Personality, Impact. Springer, Cham. https://doi.org/10.1007/978-3-319-96154-5_7
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