In this presentation, I discuss the community associated with Abstract State Machines (ASM), especially in the context of a Community of Practice (CoP), a social science concept, considering the development of ASM by its community of researchers and practitioners over time. I also consider the long-term historical context of the advisor tree of Egon Börger, the main promulgator of the ASM approach, which can be considered as multiple interrelated CoPs, distributed over several centuries. This includes notable mathematicians and philosophers among its number with some interesting links between the people involved. Despite most being active well before the inception of computer science, a number have been influential on the field.

1. Communities and Ancestors
associated with
Egon Börger and ASM
Prof. Jonathan P. Bowen FRSA FBCS
Emeritus Professor of Computing
London South Bank University
Adjunct Professor
Southwest University
Chongqing, China
Chairman of Museophile Limited
www.jpbowen.com

2. • Talk in Oxford (September 1993)
• ProCoS projects and Working
Group (January 1995)
• ZUM’97 keynote & ProCoS-WG meeting
in Reading, UK (April 1997)
Background (1990s)

3. • BCS-FACS Workshop on
Teaching Formal Methods,
Oxford (December 2003)
• Software Specification Methods
book Z/ASM case studies (2006)
• 60th Festkolloquium at Schloss
Dagstuhl, Germany – Rigorous
Methods for Software
Construction and
Analysis (May 2006)
Background (2000s)

4. • Talk on ASM at BCS, London
for BCS-FACS (March 2007)
• ABZ 2008 Conference, London,
co-chairs – first conference on
ASM, B-Method, Z notation,
etc. (September 2008)
• Conference series continues to
this day – ABZ 2021 this week
online (June 2021)
Background (2000s)

5. • Formal Methods: State of the
Art and New Directions book
(2010)
• Formal Aspects of Computing
(FAC) journal ABZ 2008
special issue (January 2011)
• Review of Modeling
Companion for Software
Practitioners book for FAC
journal (November 2018)
Background (2010s)

6. Community of Practice
(CoP)
• Social sciences concept
• Wenger, E.: Communities of
Practice: Learning, Meaning, and
Identity. Cambridge University
Press, Cambridge (1998)
• Wenger, E., McDermott, R.A.,
Snyder, W.: Cultivating
Communities of Practice: A guide
to managing knowledge. Harvard
Business School Press, Boston
(2002)

7. CoPs and formal methods
• Community of Practice (CoP)
– collection of people developing domain
knowledge
• Formal methods communities
– ASM, B, Z, etc., researchers and users
“Reason is purposive activity.”
— Georg Hegel (1770–1831)

8. Various formal methods CoPs!
Z
???

9. Elements of a CoP
• Domain of knowledge and interest
– Abstract State Machines
• Community around this domain
– researchers, practitioners, committees, etc.
• Practice of the community in this domain
– software engineering, formal specification
ABZ 2018, Southampton, UK

10. Stages of a CoP (1)
• Potential: An existing network of people to
initiate a CoP. For ASM, formal methods
researchers. Progenitors: Yuri Gurevich
and Egon Börger.
• Coalescing: Establish a rhythm to ensure
its continuation. For ASM, early workshops.
• Maturing: The community must become
more enduring. For ASM, regular ABZ
conferences, published books, etc.

11. Stages of a CoP (2)
• Stewardship: The community must
respond to its environment and develop.
ASM collaborates with other state-based
formal methods like Alloy, B, TLA, VDM,
and Z, through ABZ.
• Legacy: All communities end eventually,
if successful morphing into further
communities. The ASM community
should plan for this!

12. Cultivating a CoP
1. Design the CoP to evolve naturally.
2. Create opportunities for open
discussion. Meetings, especially
ABZ.
“The art of community development is to use the
synergy between domain, community, and
practice to help a community evolve and fulfil its
potential.” – Wenger et al. (2002)

13. 3. Welcome and allow different levels
of participation.
• Develop ASM – researchers
• Learn ASM – students
• Use ASM – industry
• Read ASM – testers,
implementers
• Write ASM – specifiers
• Appreciate ASM –
managers

14. 4. Develop both public and
private CoP facilities.
• ASM workshops
(now ABZ conference)
• ASM information
• ASM books
• ASM courses/tutorials

15. 5. Focus on the value of the CoP.
“The challenge of designing natural structures like
communities of practice is creating an approach to
design that redefines design itself”
– Wenger et al. (2002)
6. Combine familiarity and excitement
within the CoP.
7. Find and nurture a regular rhythm for
the CoP. ABZ this week.

16. The Development of ASM
• 1980s: Yuri Gurevich and “evolving
algebras” – ASM thesis
• 1990s: Research community, led by
Egon Börger – ASM models for C,
Java, Prolog, SDL, UML, VHDL, etc.
• 2000s: 1st book (2003), ABZ (2008…).
• 2010s: 2nd book (2018), ABZ continues.
• 2020s: 3rd book?! ABZ…

17. Some key ASM publications

18. Author influences of Egon Börger
(Semantic Scholar: http://www.semanticscholar.org)

19. Mentions of Egon Börger in books
(Ngram Viewer, Google Books: http://books.google.com/ngrams)
1970 1980 1990 2000 2010 2020

20. Mentions of Abstract State Machines in books
(Ngram Viewer, Google Books: http://books.google.com/ngrams)
1980 1990 2000 2010 2020

21. Academic advisor tree for Egon Börger (1)
(Mathematics Genealogy Project: https://www.mathgenealogy.org)

22. Doctoral thesis & Dieter Rödding
Reduktionstypen in Krom- und Hornformeln
(English: “Reduction types in Krom and Horn
formulas”), from Westfälische Wilhelms-
Universität Münster (1971)
– supervised by Dieter Rödding (1937–1984)
– mathematical logician: classification
of recursive functions, recursive
types in predicate logic.
– machine-oriented approach to
complexity (pre “computer science”).
– doctoral thesis: Münster (1961),
under Gisbert Hasenjaeger.

23. Gisbert Hasenjaeger (1919–2006)
• Mathematical logician
• Assistant to logician Heinrich Scholz
(1884–1956) at Cipher Department of
Wehrmacht High Command.
• WW II: Responsible for security of
Enigma machine, used for encrypting
German messages.
• 1945–50: Doctorate with Heinrich
Scholz, Münster.
• 1949: Proof for completeness theorem
of Kurt Gödel (1906–1978) for
predicate logic.

24. Hasenjaeger and Turing
• 1963: Constructed a universal Turing machine
(UTM) from telephone relays.
• 1970s: Learned about breaking of Enigma at
Bletchley Park by Alan Turing et al.
• Below: UTM artefacts from Hasenjaeger’s
“Turing Room”, used for teaching at Münster.
• Saved by his student Dieter Rödding and now in
the Heinz Nixdorf Museum, Paderborn.

25. Heinrich Scholz (1884–1956)
• Logician, philosopher, theologi[ci]an
• Two advanced degrees:
– Licentiate in theology, Humboldt-Universität zu
Berlin (1909)
– Doctor of Philosophy, Friedrich-Alexander-
Universität Erlangen-Nürnberg (1913)
• Requested a preprint of Turing’s 1936
paper “On Computable Numbers”.
• Presented Turing‘s paper at a seminar.
• Worked at Cipher Department of
Wehrmacht High Command with
Gisbert Hasenjaeger as an assistant.

26. Karl Mollweide (1774–1825)
• Mathematician and astronomer
• Student of Johann Pfaff (1765–1825)
• Invented Mollweide projection for maps
• Mollweide's formula in trigonometry for triangles
Online talk by
Roger Penrose,
in celebration of
his 2020 Nobel
Prize

27. Other students of Johann Pfaff
• Carl Gauss (1777–1855), physicist,
Gaussian distribution, etc.
• August Möbius (1790–1888),
theoretical astronomer, Möbius strip

28. Georg Hegel (1770–1831)
• Philosopher
• Dissertation: Quid intersit inter
Philosophiam et Theologiam
(“What is the difference between
Philosophy and Theology”), Jena (1801).
• Leading figure in German idealism, developed
from ideas of Immanuel Kant.
• Science of Logic (1812–16), idea of logic as a
system of dialectics, dubbed Hegelian dialectic:
– thesis, antithesis, resolved by synthesis
“To comprehend what is, is the task of philosophy:
and what is is Reason.” – Georg Hegel

29. Academic advisor tree for Egon Börger (2)
(MGP; blue arrows indicate family connections)

30. Immanuel Kant (1724–1804)
• Philosopher
• Studied philosophy of Gottfried Leibniz
with Martin Knutzen (1713–1751),
Extraordinary Professor of Logic and
Metaphysics
• Age of Enlightenment (aka Age of
Reason) – works covering aesthetics,
epistemology, ethics, metaphysics, etc.
“All our knowledge begins with the senses,
proceeds then to the understanding, and ends with
reason. There is nothing higher than reason.”
– Immanuel Kant

31. Otto Mencke (1644–1707)
• Philosopher and scientist, Leipzig
• Studied under Jakob Thomasius (1622–
1684), also advisor of Gottfried Leibniz
• Brother-in-law Christoph Pfautz (1645–
1711), astronomer, geographer, librarian,
and mathematician
• Pfautz and Leibniz were advisers at Leipzig
of Christian von Wolff (1679–1754)
• 1680: Pfautz took Mencke to Holland and
England, meeting scientists including Isaac
Newton (1642–1727)
• 1682: Mencke founded the first German
scientific journal with Pfautz:
– Acta Eruditorum

32. Gottfried Leibniz (1646–1716)
• Logician, mathematician,
philosopher, polymath
• Enlightenment – rationalism
• Father: Friedrich Leibniz (1597–1652)
– “Grandfather” advisor
• Ideas origin of Entscheidungsproblem
(decision problem) as tackled by Turing
• Binary arithmetic – computers
“There are two kinds of truths: those of reasoning and those
of fact. The truths of reasoning are necessary and their
opposite is impossible; the truths of fact are contingent and
their opposites are possible.” – Gottfried Leibniz

33. Binary arithmetic (Leibniz, 1703)
“There are 10 types of people: those that can
count in binary and those that can’t.” – Anon.

34. Further advisor relationships
• David Hilbert (1862–1943),
via Johann Pfaff and Gauss
• Alan Turing (1912–1954), via
Gottfried Leibniz and Nicolas
Malebranche (1638–1715)
• Yuri Gurevich, via Russian
mathematician Pafnuty
Chebyshev (1821–1894) and
Johann Pfaff

35. Finally:
The Last Supper
Extensive restoration:
Zoom call!

36. Thank you Egon!
Prof. Jonathan Bowen
FBCS, FRSA
jonathan.bowen@lsbu.ac.uk
www.jpbowen.com
“Genius is the ability to
independently arrive at and
understand concepts that
would normally have to be
taught by another person.”
– Immanuel Kant (1724–1804)