Skip to main content
SpringerLink
Log in
Book cover

Net Theory and Applications pp 21–163Cite as

Elements of general net theory

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 84))

Abstract

Some of the main features of a theory of systems in which the concept of concurrency plays a central role are presented. This theory is founded upon a systems model called condition/event-systems (CE-systems).

In order to enrich the language concerning CE-systems, three types of completions are carried out. Completion w.r.t. information flow enables us to explicate conflict resolution and brings the notion of information into the theory. T-completion and S-completion lead to a systematic classification of all system invariants, the enloqic structure and the synchronic structure of CE-systems. The relationship between logic and net theory obtained through the enlogic structure is further exploited in a number of different ways. Similarly, the concept of synchronic distance is generalized and applied more directly to the study of systems.

From the point of view of applications, it is important to develop a family of net based models. Two such models are exhibited, bipolar synchronization systems and predicate/transiton-nets. The question as to what is meant by a family of net based models is is studied by presenting the category of nets.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anderson, A.R.: The Formal Analysis of Normative Systems. In The Logic of Action and Decision, ed. Rescher, N., Pittsburgh: The University of Pittsburgh Press, 1967

    Google Scholar 

  2. Blanchard, M.: Le GRAFCET pour une Representation Normalisee de Cahier des Charges d'un Automatisme Logique. Automatique et Informatique Industrielle, No. 61, pp. 27–32 + No. 62, pp. 36–40 (1977)

    Google Scholar 

  3. Best, E.: A Theorem on the Characteristics of Non-Sequential Processes. Computing Laboratory Technical Report No. 116, University of Newcastle-upon-Tyne (1977)

    Google Scholar 

  4. Chaney, T.J.; Ornstien, S.M.; Littlefield, W.M.: Beware the Synchronizer. COMPCON-72, IEEE Computer Society Conference, pp. 12–14, 1972

    Google Scholar 

  5. Chang, C.; Lee, R.: Symbolic Logic and Mechanical Theorem Proving. New York, London: Academic Press, 1973

    Google Scholar 

  6. Commoner, F.; Holt, A.W.; Even, S.; Pnueli, A.: Marked Directed Graphs. J. Computer and System Sc. 5, 511–523 (1971)

    Google Scholar 

  7. Constable, R.L.: On the Theory of Programming Logics. Proc. ACM STOC 9, pp. 269–285 (1977)

    Google Scholar 

  8. Darlington, J.L.: A Net Based Theorem Proving Procedure for Program Verification and Synthesis. In Proc. of the 4th Workshop on Artificial Intelligence, Bad Honnef. Institut für Informatik, Universität Bonn, 1979

    Google Scholar 

  9. Ellis, C.A.: Consistency and Correctness of Duplicate Database Systems. Proc. of the 6th Symposium on Operating System Principles, Purdue University, Nov. 1977, ACM Operating Systems Review Vol. 11, Nr. 5, 1977

    Google Scholar 

  10. van Emde Boas, P.: The Connection Between Modal Logic and Algorithmic Logics. In Mathematical Foundations of Computer Science, ed. Winkowski, J., Lecture Notes in Computer Science 64, pp. 1–15, Berlin, Heidelberg, New York: Springer, 1978

    Google Scholar 

  11. Fernandez, C.: Net Topology I, II. ISF-Reports 75.09, 76.02, St.Augustin: Gesellschaft für Mathematik und Datenverarbeitung, 1975, 1976

    Google Scholar 

  12. Fischer, M.J.; Ladner, R.E.: Propositional Modal Logic of Programs. Proc. ACM STOC 9, pp. 286–294, 1977

    Google Scholar 

  13. Genrich, H.J.; Lautenbach, K.: Synchronisationsgraphen. Acta Informatica 2, 143–161 (1973)

    Article  Google Scholar 

  14. Genrich, H.J.: Extended Simple Regular Expressions. In Mathematical Foundations of Computer Science, ed. Becvar, J., Lecture Notes in Computer Science 32, pp. 231–237, Berlin, Heidelberg, New York: Springer, 1975

    Google Scholar 

  15. Genrich, H.J.: Ein systemtheoretischer Beitrag zur Handlungslogik. ISF-Report 75.03, St.Augustin: Gesellschaft für Mathematik und Datenverarbeitung, 1975

    Google Scholar 

  16. Genrich, H.J.: The Petri Net Representation of Mathematical Knowledge. ISF-Report 76.05, St.Augustin: Gesellschaft für Mathematik und Datenverarbeitung, 1976

    Google Scholar 

  17. Genrich, H.J.: Ein Kalkül des Planens und Handelns. In Ansätze zur Organisationstheorie rechnergestützter Informationssysteme, ed. Petri, C.A., Berichte der Gesellschaft für Mathematik und Datenverarbeitung 111, pp.77–92, München, Wien: R. Oldenbourg 1979

    Google Scholar 

  18. Genrich, H.J.; Lautenbach, K.: Facts in Place/Transition-Nets. In Mathematical Foundations of Computer Science, ed. Winkowski, J., Lecture Notes in Computer Science 64, pp. 213–231, Berlin, Heidelberg, New York: Springer, 1978

    Google Scholar 

  19. Genrich, H.J.; Lautenbach, K.: The Analysis of Dristibuted Systems by Means of Predicate/Transition-Nets. In Semantics of Concurrent Computation, ed. Kahn, G., Lecture Notes in Computer Science 70, pp. 123–146, Berlin, Heidelberg, New York: Springer, 1979

    Google Scholar 

  20. Genrich, H.J.; Thieler-Mevissen, G.: The Calculus of Facts. In Mathematical Foundations of Computer Science, ed. Mazurkiewicz, A., Lecture Notes in Computer Science 45, pp. 588–595, Berlin, Heidelberg, New York: Springer, 1976

    Google Scholar 

  21. Hack, M.: Analysis of Production Schemata by Petri Nets. MIT-Project MAC, TR-94 (1972)

    Google Scholar 

  22. Harel, D.; Meyer, A; Pratt, V.R.: Computability and Completeness in Logics of Programs. Proc, ACM STOC 9, pp. 261–268 (1977)

    Google Scholar 

  23. Herstein, I.N.: Topics in Algebra, 2nd Edition. Lexington, Toronto: Xerox College Publishing, 1975

    Google Scholar 

  24. Holt, A.W.: Net Models of Organizational Systems, in Theory and Practice. In Ansätze zur Organisationstheorie rechnergestützter Informationssysteme, ed. Petri, C.A., Berichte der Gesellschaft für Mathematik und Datenverarbeitung 111, pp. 39–62, München, Wien: R. Oldenbourg, 1979

    Google Scholar 

  25. Holt, A.W.; Commoner, F.: Events and Conditions. Report of the Project MAC Conference on Concurrent Systems and Parallel Computation, pp. 3–52, 1970

    Google Scholar 

  26. Holt, A.W. et al.: Information System Theory Project: Final Report. Princeton, N.J.: Applied Data Research Inc., RADC-TR-68-305, NTIS AD 676972, 1968

    Google Scholar 

  27. Jump, J.R.; Thiagarajan, P.S.: On the Equivalence of Asynchronous Control Structures. SIAM Journal on Computing, 2, No.2, 67–87 (1973)

    Article  Google Scholar 

  28. Kahn, G.; Plotkin, G.D.: Domains Concrets. IRIA Rapport de Recherche No. 336, Le Chesnay: IRIA, 1978

    Google Scholar 

  29. Kripke, S.: Semantical Considerations on Modal Logic. Acta Philosophica Fennica 16, pp. 83–94 (1963)

    Google Scholar 

  30. Lautenbach, K.: Exakte Bedingungen der Lebendigkeit für eine Klasse von Petri-Netzen. Berichte der GMD 82, St. Augustin: Gesellschaft für Mathematik und Datenverarbeitung Bonn, 1973

    Google Scholar 

  31. Lautenbach, K.: Ein kombinatorischer Ansatz zur Beschreibung und Erreichung von Fairness in Scheduling-Problemen. In Applied Computer Science 8, ed. Mühlbacher, J., München, Wien: Verlag Carl Hanser, 1977

    Google Scholar 

  32. Lautenbach, K.; Schmid, H.A.: Use of Nets for Proving Correctness of Concurrent Process Systems. Proceedings of IFIP Congress 74, North Holland Publ. Comp., 1974

    Google Scholar 

  33. Lautenbach, K; Wedde, H.: Generating Control Mechanisms by Restrictions. In Mathematical Foundations of Computer Science, ed. Mazurkiewicz, A, Lecture Notes in Computer Science 45, pp. 416–422, Berlin, Heidelberg, New York: Springer, 1976

    Google Scholar 

  34. Mac Lane, S.: Categories for the Working Mathematician. New York, Heidelberg, Berlin: Springer, 1971

    Google Scholar 

  35. Meldman, J.: A Petri-Net Representation of Civil Procedure. IDEA: The Journal of Law and Technology, 19, no. 2, pp.123–148 (1978)

    Google Scholar 

  36. Milne, G.J.: Modelling Distributed Database Protocolls by Synchronisation Processes (Draft Version, Nov. 1978), Department of Computer Science, Edinburgh University

    Google Scholar 

  37. Mirkowska, G.: Algorithmic Logic and its Application in the Theory of Programs. Fundamenta Informaticae 1, pp: 1–17, 147–165 (1977)

    Google Scholar 

  38. Nutt, G.J.: The Formulation and Application of Evaluation Nets. Thesis, Computer Science Group, University of Washington, Seattle (1972)

    Google Scholar 

  39. Parikh, R.: The Completeness of Propositional Dynamic Logic. In Mathematical Foundations of Computer Science, ed. Winkowski, J., Lecture Notes in Computer Science 64, pp. 403–415, Berlin, Heidelberg, New York: Springer, 1978

    Google Scholar 

  40. Parikh, R.: A Decidability Result for a Second Order Process Logic. MIT/LCS/TM-112, Cambridge, Mas.: MIT Laboratory for Computer Science, 1978

    Google Scholar 

  41. Patil, S.S.: Coordination of Asynchronous Events. MIT, Project MAC, Technical Report 72, Cambridge, Mass., 1970

    Google Scholar 

  42. Patil, S.S.: Synchronizers and Arbiters. Computation Structures Group Memo 91, Project MAC, M.I.T., Cambridge, Mass., 1972

    Google Scholar 

  43. Petri, C.A.: Fundamentals of a Theory of Asynchronous Information Flow. In Proceedings of IFIP Congress 62, North-Holland Publ. Comp., Amsterdam

    Google Scholar 

  44. Petri, C.A.: Kommunikation mit Automaten. Bonn: Institut für Instrumentelle Mathematik, Schriften des IIM Nr. 2, 1962

    Google Scholar 

  45. Petri, C.A.: Grundsätzliches zur Beschreibung diskreter Pozesse. 3. Colloguium über Automathentheorie, Basel: Birkhäuser Verlag, 1967

    Google Scholar 

  46. Petri, C.A.: Concepts of Net Theory. Mathematical Foundations of Computer Science, Math. Institute of the Slovak Ac. of Sciences, 1973

    Google Scholar 

  47. Petri, C.A.: Non-Sequential Processes. ISF-Report 77.05, St. Augustin: Gesellschaft für Mathematik und Datenverarbeitung, 1975

    Google Scholar 

  48. Petri, C.A.: Interpretations of Net Theory. ISF-Report 75.07, St. Augustin: Gesellschaft für Mathematik und Datenverarbeitung, 1975

    Google Scholar 

  49. Petri, C.A.: General Net Theory. Computing System Design: Proceedings of the Joint IBM University of Newcastle upon Tyne Seminar, Sept. 1976 / Shaw, B. (Ed.), University of Newcastle upon Tyne (1977)

    Google Scholar 

  50. Petri, C.A.: Concurrency as a Basis for System Thinking. ISF-Report 78.06, St. Augustin: Gesellschaft für Mathematik und Datenverarbeitung, 1978

    Google Scholar 

  51. Pnueli, A.: The Temporal logic of Programs. Proc. IEEE FOCS 48, pp. 46–57 (1977)

    Google Scholar 

  52. Rescher, N. (ed.): The Logic of Action and Decision. Pittsburgh: The University of Pittsburgh Press, 1967

    Google Scholar 

  53. Schiffers, M.: Behandlung eines Synchronisationsproblems mit gefärbten Petri-Netzen. Universität Bonn, Diplomarbeit (1977)

    Google Scholar 

  54. Schiffers, M; Wedde, H.: Analyzing Program Solutions of Coordination Problems by CP-nets. Mathematical Foundations of Computer Science 1978 / Winkowski, J. (Ed.), Berlin, Heidelberg, New York: Springer Verlag (1978)

    Google Scholar 

  55. Shapiro, R.M.: Towards a Design Methodology for Information Systems. In Ansätze zur Organisationstheorie rechnergestützter Informationssysteme, ed. Petri, C.A., Berichte der Gesellschaft für Mathematik und Datenverarbeitung 111, pp. 107–118, München, Wien: R. Oldenbourg 1979

    Google Scholar 

  56. Shapiro, R.M.; Saint, H.: The Representation of Algorithms. Applied Data Research, Inc., Final Techn. Report RADC-TR-69-313, Vol. 2, NTIS AD 697026, New York, 1969

    Google Scholar 

  57. Shapiro, R.M.; Thiagarajan, P.S.: On the Maitenance of Distributed Copies of a Database. St. Augustin: Gesellschaft für Mathematik und Datenverarbeitung Bonn, Interner Benicht ISF-78-04 (1978)

    Google Scholar 

  58. Thiagarajan, PS.: Genrich, H.J.: Assignment Systems — A Model for Asynchronous Computations. ISF-Report 76.10, St. Augustin: Gesellschaft für Mathematik und Datenvenarbeitung, 1976

    Google Scholar 

  59. Thieler-Mevissen, G.: The Petri Net Calculus of Predicte Logic. ISF-Report 76.09, St. Augustin: Gesellschaft für Mathematik und Datenverarbeitung, 1976

    Google Scholar 

  60. Thieler-Mevissen, G.: Die Struktur der Violations eines Systems. ISF-Report 78.01, St. Augustin: Gesellschaft für Mathematik und Datenverarbeitung, 1978

    Google Scholar 

  61. Wedde, H.: Lose Kopplung von Systemkomponenten. Bericht der GMD 96, St.Augustin: Gesellschaft für Mathematik und Datenverarbeitung, 1975

    Google Scholar 

  62. von Wright, G.H.: And Next. Acta Philosophica Fennica 18, pp. 293–304, Helsinki 1965

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informationssystemforschung (ISF) Gesellschaft für Mathematik und Datenverarbeitung Schloss Birlinghoven, D-5205, St.Augustin 1

    H. J. Genrich, K. Lautenbach & P. S. Thiagarajan

Authors
  1. H. J. Genrich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Lautenbach
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. S. Thiagarajan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Wilfried Brauer

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Genrich, H.J., Lautenbach, K., Thiagarajan, P.S. (1980). Elements of general net theory. In: Brauer, W. (eds) Net Theory and Applications. Lecture Notes in Computer Science, vol 84. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10001-6_22

Download citation

  • DOI: https://doi.org/10.1007/3-540-10001-6_22

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10001-0

  • Online ISBN: 978-3-540-39322-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation