Skip to main content
SpringerLink
Log in

Petri nets and other models of concurrency

  • III Relationship to Other Models
  • Chapter
  • First Online:
Lectures on Petri Nets I: Basic Models (ACPN 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1491))

Included in the following conference series:

Abstract

This paper retraces, collects, and summarises contributions of the authors — in collaboration with others — on the theme of Petri nets and their categorical relationships to other models of concurrency.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Abramsky (1996), Retracing Some Paths in Process Algebra, in Proceedings of CONCUR 96, U. Montanari and V. Sassone (Eds.), Lecture Notes in Computer Science1119, 1–17, Springer-Verlag.

    Google Scholar 

  2. E.S. Bainbridge (1976), Feedback and Generalized Logic. Information and Control31, 75–96.

    Google Scholar 

  3. J. Bénabgu (1963), Categories with Multiplication. Comptes Rendus Académie Science Paris256, 1887–1890.

    Google Scholar 

  4. M.A. Bednarczyk (1987), Categories ofAsynchronous Systems. PhD thesis, University of Sussex, Report 1/88, School of Cognitive and Computing Sciences, University of Sussex.

    Google Scholar 

  5. D. Benson and O. Ben-Shachar (1988), Bisimulation of Automata. Information and Computation79, 60–83, Academic Press.

    Google Scholar 

  6. G. Berry (1979), Modèles completement adéquats et stables des λ-calculs typèes. Thèse de Doctorat d'Etat, Université Paris VII.

    Google Scholar 

  7. E. Best and R. Devillers (1987), Sequential and Concurrent Behaviour in Petri Net Theory. Theoretical Computer Science55, 87–136, Elsevier.

    Google Scholar 

  8. E. Best, R. Devillers, and J. Hall (1992), The Petri Box Calculus: a New Causal Algebra with Multilabel Communication, in Advances in Petri Nets 92, G. Rozenberg (Ed.), Lecture Notes in Computer Science609, 21–69, Springer-Verlag.

    Google Scholar 

  9. E. Best and C. Fernandez (1988), Non-sequential Processes: A Petri Net View. EATCS Monographs on Theoretical Computer Science 13, Springer-Verlag.

    Google Scholar 

  10. S.L. Bloom and Z. Ésik (1991), Iteration Theories: the Equational Logic of Iterative Processes. EATCS Monographs on Theoretical Computer Science 30, Springer-Verlag.

    Google Scholar 

  11. C. Brown and D. Gurr (1992), Temporal Logic and Categories of Petri Nets, in Proceedings of ICALP 93, A. Lingas et al. (Eds.), Lecture Notes in Computer Science700, 570–581, Springer-Verlag.

    Google Scholar 

  12. C. Brown, D. Gurr, and V. de Paiva (1991), A Linear Specification Language for Petri Nets. Technical Report DAIMI PB-363, Computer Science Dept., University of Aarhus.

    Google Scholar 

  13. J. Bruno and S.M. Altman (1971), A Theory of Asynchronous Control Networks. IEEE Transactions on Computers, Vol. C-20, 629–638, IEEE Press.

    Google Scholar 

  14. I. Castellani (1985), Bisimulation and Abstraction Homomorphisms, in Proceedings of CRAP 85, H. Ehrig et al. (Eds.), Lecture Notes in Computer Science185, 223–238, Springer-Verlag.

    Google Scholar 

  15. G.L. CATTANI, M. FIORE, AND G. WINSKEL (1998), A Theory of Recursive Domains with Applications to Concurrency, in Proceedings of the 13th LICS Symposium, IEEE Press. To appear.

    Google Scholar 

  16. P. Degano, R. De Nicola, and U. Montanabi (1987). Observational Equivalences for Concurrency Models, in Formal Description of Programming Concepts—III, IFIP, M. Wirsing (Ed.), 105–132, Elsevier.

    Google Scholar 

  17. P. Degano, R. De Nicola, and U. Montanabi (1988), A Distributed Operational Semantics for CCS based on Condition/Event Systems. Acta Informatica26, 59–91, Springer-Verlag.

    Google Scholar 

  18. P. Degano, J. Meseguer, and U. Montanabi (1989), Axiomatizing Net Computations and Processes, in Proceedings of the 4th LICS Symposium, 175–185, IEEE Press.

    Google Scholar 

  19. J.B. Dennis (1970), Modular, Asynchronous Control Structures for a High Performance Processor, in Record of the Project MAC Conference on Concurrent Systems and Parallel Computation, ACM Press.

    Google Scholar 

  20. A. Ehrenfeucht and G. Rozenberg (1987), On the Structure of Dependence Graphs, in Concurrency and Nets, K. Voss et al. (Eds.), 141–170, Springer-Verlag.

    Google Scholar 

  21. S. Eilenberg, and G.M. Kelly (1966), Closed Categories, in Proceedings of the Conference on Categorical Algebra, S. Eilenberg et al. (Eds.), 421–562, Springer-Verlag.

    Google Scholar 

  22. C. Elgot (1975), Monadic Computation and Iterative Algebraic Theories, in Logic Colloquium '73, H.E. Rose and J.C. Shepherdson (Eds.), 175–230, North-Holland.

    Google Scholar 

  23. G. Ferrari, U. Montanabi, and M. Mowbray (1997), Structured Transition Systems with Parametric Observations: Observational Congruences and Minimal Realizations. Mathematical Structures in Computer Science7, 241–282, Cambridge University Press.

    Google Scholar 

  24. R.J. van Glabbeek and U. Goltz (1989), Equivalence Notions for Concurrent Systems and Refinement of Actions, in Proceedings of MFCS 89, A. Kreczmar and G. Mirkowska (Eds.), Lecture Notes in Computer Science379, 237–248, Springer-Verlag.

    Google Scholar 

  25. R.J. van Glabbeek and F. Vaandrager (1987), Petri Net Models for Algebraic Theories of Concurrency, in Proceedings of RARLE, J.W. de Bakker et al. (Eds.), Lecture Notes in Computer Science259, 224–242. Springer-Verlag.

    Google Scholar 

  26. U. Goltz and W. Reisig (1983), The Non-Sequential Behaviour of Petri Nets. Information and Computation57, 125–147, Academic Press.

    Google Scholar 

  27. R. Gorrieri and U. Montanabi (1990), Scone: A Simple Calculus of Nets, in Proceedings of CONCUR 90, J.C.M. Baeten and J.W. Klop (Eds.), Lecture Notes in Computer Science458, 2–31, Springer-Verlag.

    Google Scholar 

  28. J. Grabowsky (1981), On partial languages. Annales Societatis Mathematicae PolonaeIV.2, 428–498, North-Holland.

    Google Scholar 

  29. M. Hennessy (1988), Algebraic Theory of Processes. MIT Press.

    Google Scholar 

  30. C.A.R. Hoare (1985), Communicating Sequential Processes. Prentice Hall.

    Google Scholar 

  31. M. Hasegawa (1997), Recursion from Cyclic Sharing: Traced Monoidal Categories, in Proceedings of TLCA 97, Ph. de Groote and J.R. Hindley (Eds.), Lecture Notes in Computer Science1210, 196–213, Springer-Verlag.

    Google Scholar 

  32. T.T. Hildebrandt, P. Panangaden, and G. Winskel (1998), Relational Semantics of Non-Deterministic Datallow, in Proceedings of CONCUR 98, D. Sangiorgi and R. de Simone (Eds.), Lecture Notes in Computer Science, Springer-Verlag. To appear.

    Google Scholar 

  33. P.W. Hoogers, H.C.M. Kleijn, and P.S. Thiagarajan (1992), A Trace Semantics for Petri Nets, in Proceedings of ICALP 92, W. Kuich (Ed.), Lecture Notes in Computer Science623, 595–604, Springer-Verlag.

    Google Scholar 

  34. T. Huns and M. Nielsen (1998), Timed Bisimulation and Open Maps, in Proceedings of MFCS 98, J. Gruska et al. (Eds.), Lecture Notes in Computer Science, Springer-Verlag. To appear.

    Google Scholar 

  35. xA. Joyal, M. Nielsen, and G. Winskel (1996), Bisimulation from Open Maps. Information and Computation127, 164–185, Academic Press.

    Google Scholar 

  36. A. Joyal, R. Street, and D. Verity (1996), Traced Monoidal Categories. Mathematical Proceedings of the Cambridge Philosophical Society119, 447–468. Cambridge University Press.

    Google Scholar 

  37. P. Katis, N. Sabadini, and R. Walters (1997), Bicategories of Processes. Journal of Pure and Applied Algebra115, 141–178, North-Holland.

    Google Scholar 

  38. R.M. Keller (1974), Towards a Theory of Universal Speed-Independent Modules. IEEE Transactions on Computers vol. C-23, 21–33, IEEE Press.

    Google Scholar 

  39. G.M. Kelly (1964), On MacLane's Conditions for Coherence of Natural Associativities, Commutativities, etc. Journal of Algebra1, 397–402, Acamedic Press.

    Google Scholar 

  40. G.M. Kelly and M. Laplaza (1980), Coherence for Compact Closed Categories. Journal ofPure and Applied Algebra19, 193–213, North-Holland.

    Google Scholar 

  41. S. MacLane (1963), Natural Associativity and Commutativity. Rice University Studies 49, pp. 28–46, Rice University Press.

    Google Scholar 

  42. S. MacLane (1971), Categories for the Working Mathematician. Graduate Texts in Mathematics, Springer-Verlag.

    Google Scholar 

  43. A. Mazurkiewicz (1977), Concurrent Program Schemes and their Interpretations. Technical Report DAIMI PB-78, Computer Science Dept., University of Aarhus.

    Google Scholar 

  44. A. Mazurkiewicz (1987), Trace theory, in Petri Nets, Applications and Relationship to other Models of Concurrency, W. Brauer et al. (Eds.), Lecture Notes in Computer Science255, 279–324, Springer-Verlag.

    Google Scholar 

  45. J. Meseguer and U. Montanari (1990), Petri Nets are Monoids. Information and Computation88, 105–155, Academic Press.

    Google Scholar 

  46. J. Meseguer, U. Montanari, and V. Sassone (1992), On the Semantics of Petri Nets, in Proceedings of CONCUR 92, R. Cleaveland (Ed.), Lecture Notes in Computer Science630, 286–301, Springer-Verlag.

    Google Scholar 

  47. J. Meseguer, U. Montanari, and V. Sassone (1996), Process versus Unfolding Semantics for Place/Transition Petri Nets. Theoretical Computer Science153, 171–210, Elsevier.

    Google Scholar 

  48. J. Meseguer, U. Montanari, and V. Sassone (1997), On the Semantics of Place/Transition Petri Nets. Mathematical Structures in Computer Science7, 359–397 Cambridge University Press.

    Google Scholar 

  49. R. Milner (1980), A Calculus of Communicating Systems. Lecture Notes in Computer Science 92, Springer-Verlag.

    Google Scholar 

  50. R. Milner (1989), Communication and Concurrency. Prentice-Hall.

    Google Scholar 

  51. R. Milner (1993), Action Calculi or Syntactic Action Structures, in Proceedings of MFCS 93, A. Borzyszkowski, S. Sokolowski (Eds.), Lecture Notes in Computer Science711, 105–121, Springer-Verlag.

    Google Scholar 

  52. E.H. Moore (1897), Concerning the abstract group of order k! isomorphic with the symmetric substitution group on k letters. Proceedings of the London Mathematical Society28, 357–366, Claredon Press.

    Google Scholar 

  53. M. Mukund (1992), Petri Nets and Step Transition Systems. International Journal of Foundations of Computer Science3, 443–478, World Scientific.

    Google Scholar 

  54. M. Mukund and M. Nielsen (1992), Locations and Asynchronous Transition Systems, in Proceedings of FST & TCS 92, R. Shyamasundar (Ed.), Lecture Notes in Computer Science652, 328–341, Springer-Verlag.

    Google Scholar 

  55. M. Nielsen and A. Cheng (1995), Observing Behaviour Categorically, in Proceedings of FST & TCS 95, P.S. Thiagarajan (Ed.), Lecture Notes in Computer Science1026, 263–278, Springer-Verlag.

    Google Scholar 

  56. M. Nielsen and C. Clausen (1995), Games and Logics for a Noninterleaving Bisimulation. Nordic Journal of Computing2, 222–250, Publishing Association NJC.

    Google Scholar 

  57. M. Nielsen, G. Plotkin, and G. Winskel (1981), Petri Nets, Event Structures and Domains, Part 1. Theoretical Computer Science13, 85–108, Elsevier.

    Google Scholar 

  58. M. Nielsen, L. Prisse, and V. Sassons (1995), Characterizing Behavioural Congruences for Petri Nets, in Proceedings of CONCUR 95, I. Lee and S. Smolka (Eds.), Lecture Notes in Computer Science962, 175–189, Springer-Verlag.

    Google Scholar 

  59. M. Nielsen, G. Rozenberg, and P.S. Thiagarajan (1990), Behavioural Notions for Elementary Net Systems. Distributed Computing4, 45–57. Springer-Verlag.

    Google Scholar 

  60. M. Nielsen, G. Rozenberg, and P.S. Thiagarajan (1992), Elementary Transition Systems. Theoretical Computer Science96, 3–33, Elsevier.

    Google Scholar 

  61. M. Nielsen, G. Rozenberg, and P.S. Thiagarajan (1995), Transition Systems, Event Structures and Unfoldings. Information and Computation118, 191–207, AcademicPress.

    Google Scholar 

  62. M. Nielsen and G. Winskel (1995), Trace Structures and other Models for Concurrency, in The Book of Traces, V. Diekert and G. Rozenberg (Eds.), 271–306, World Scientific.

    Google Scholar 

  63. M. Nielsen and G. Winskel (1996), Petri Nets and Bisimulation. Theoretical Computer Science153, 211–244, Elsevier.

    Google Scholar 

  64. E.R. Olderog (1987), A Petri Net Semantics for CCSP, in Advances in Petri Nets 86, W. Brauer et al. (Eds.), Lecture Notes in Computer Science255, 196–223, 5pringer-Verlag.

    Google Scholar 

  65. E.R. Olderog (1991), Nets, Terms and Formulas. Cambridge Tracts in Theoretical Computer Science, Cambridge University Press.

    Google Scholar 

  66. C.A. Petri (1962), Kommunikation mit Automaten. PhD thesis, Institut für Instrumentelle Mathematik, Bonn.

    Google Scholar 

  67. C.A. Petri (1973), Concepts of Net Theory, in Proceedings of MFCS 73, 137–146, Mathematics Institute of the Slovak Academy of Science.

    Google Scholar 

  68. C.A. Petri (1977), Non-Sequential Processes. Interner Bericht ISF-77-5, Geselischaft für Mathematik and Datenverarbeitung, Bonn.

    Google Scholar 

  69. V. Pratt (1986), Modelling Concurrency with Partial Orders. International Journal of Parallel Programming15, 33–71. Plenum.

    Google Scholar 

  70. L. Prisse (1983), Automata and Concurrency. Theoretical Computer Science25, 221–265, Elsevier.

    Google Scholar 

  71. A. Rabinovitch and B. Trakhtenbrot (1988), Behaviour structures and nets. Fundamenta Informatica11, 357–404, North-Holland.

    Google Scholar 

  72. W. Reisig (1985), Petri Nets (an Introduction). EATCS Monographs on Theoretical Computer Science 4, Springer-Verlag.

    Google Scholar 

  73. G. Rozenberg (1987), Behaviour of Elementary Net Systems, in Advances in Petri Nets 86, W. Brauer et al. (Eds.), Lecture Notes in Computer Science 254, 60–94, Springer-Verlag.

    Google Scholar 

  74. B. Rozoy and P.S. Thiagarajan (1991), Event Structures and Trace Monoids. Theoretical Computer Science91, 285–313, Elsevier.

    Google Scholar 

  75. V. Sassone (1995), Axiomatizing Petri Net Concatenable Processes, in Proceedings of FCT 95, H. Reichel (Ed.), Lecture Notes in Computer Science962, 414–423, Springer-Verlag

    Google Scholar 

  76. V. Sassone (1995), On the Category of Petri Net Computations, in Proceedings of TAPSOFT 95, P Mosses et al. (Eds.), Lecture Notes in Computer Science 915, 334–348. Springer-Verlag.

    Google Scholar 

  77. V. Sassone (1996), An Axiomatization of the Algebra of Petri Net Concatenable Processes. Theoretical Computer Science170, 277–296, Elsevier.

    Google Scholar 

  78. V. Sassone (1998), An Axiomatization of the Category of Petri Net Computations. Mathematical Structures in Computer Science8, 117–151, Cambridge University Press.

    Google Scholar 

  79. V. Sassone, M. Nielsen, and G. Winskel (1993), Deterministic Behavioural Models for Concurrency, in Proceedings of MFCS 93 A. Borzyszkowski, S. Sokolowski (Eds.), Lecture Notes in Computer Science711, 682–692, Springer-Verlag.

    Google Scholar 

  80. V. Sassone, M. Nielsen, and G. Winskel (1996), Models for Concurrency: Towards a Classification. Theoretical Computer Science170, 297–348, Elsevier.

    Google Scholar 

  81. D. Scott (1970), Outline of a Mathematical Theory of Computation, in Proceedings of 4th Annual Princeton Conference on Information Science and Systems, 169–176, Princeton University Press.

    Google Scholar 

  82. K. Segerberg (1968), Decidability of S4.1. Theoria34,7–20, Gordon and Breach.

    Google Scholar 

  83. M.W. Shields (1985), Concurrent machines. Computer Journal28, 449–465, Cambridge University Press.

    Google Scholar 

  84. E.W. Stark (1989), Concurrent Transition Systems. Theoretical Computer Science64, 221–269, Elsevier.

    Google Scholar 

  85. G. Ştefaněscu (1987), On Flowchart Theories: Part 1. The Deterministic Case. Journal of Computer and System Sciences35, 163–191, Academic Press.

    Google Scholar 

  86. G. Ştefaněscu (1987), On Flowchart Theories: Part 1. The Nondeterministic Case. Theoretical Computer Science52, 307–340, Elsevier.

    Google Scholar 

  87. P.S. Thiagarajan (1987), Elementary Net Systems, in Advances in Petri Nets 86, W. Brauer et al. (Eds.), Lecture Notes in Computer Science254, 26–59, Springer-Verlag.

    Google Scholar 

  88. J. Van Bentham (1984), Correspondence Theory, in Handbook of Philosophical Logic vol. 2, P. Gabbay and F. Guenthner (Eds.), 167–247, Reidel.

    Google Scholar 

  89. W. Vogler (1991), Deciding History Preserving Bisimilarity. in Proceedings of ICALP 91, J. Leach Albert et al. (Eds.), Lecture Notes in Computer Science510, 495–505. Springer-Verlag.

    Google Scholar 

  90. G. Winskel (1982), Event Structure Semantics for CCS and related languages, in Proceedings of the 9th ICALP, M. Nielsen and E.M. Schmidt (Eds.), Lecture Notes in Computer Science140, 561–576, Springer-Verlag.

    Google Scholar 

  91. G. Winskel (1984), A New Definition of Morphism on Petri Nets, in Proceedings of STACS 84, M. Fontet and K. Mehlhom (Eds.), Lecture Notes in Computer Science166, 140–150, Springer-Verlag.

    Google Scholar 

  92. G. Winskel (1984), Categories of Model for Concurrency, in Seminar on Concurrency, S. Brookes et al. (Eds.), Lecture Notes in Computer Science197, 246–267, Springer-Verlag.

    Google Scholar 

  93. G. Winskel (1987), Petri Nets, Algebras, Morphisms and Compositionality. Information and Computation72, 197–238, Academic Press.

    Google Scholar 

  94. G. Winskel (1986), Event Structures, in Advances in Petri Nets86, W. Brauer et al. (Eds.), Lecture Notes in Computer Science255, 325–392. Springer-Verlag.

    Google Scholar 

  95. G. Winskel (1988), An Introduction to Event Structures, in Linear time, branching time, and partial order in logics and models for concurrency, J.W. de Bakker et al. (Eds.), Lecture Notes in Computer Science354. 365–397. Springer-Verlag.

    Google Scholar 

  96. G. Winskel (1996), A Presheaf Semantics of Value-Passing Processes, in Proceedings of CONCUR 96, U. Montanari and V Sassone (Eds.), Lecture Notes in Computer Science1119, 98–114, Springer-Verlag.

    Google Scholar 

  97. G. Winskel and M. Nielsen (1995), Models for Concurrency, in Handbook of Logic in Computer Science vol. 4, S. Abramsky et al. (Eds), 1–148, Oxford University Press.

    Google Scholar 

  98. G. Winskel and M. Nielsen (1997), Presheaves as Transition Systems, in Proceedings of POMIV 96, D. Peled et al. (Eds.), DIMACS Series in Discrete Mathematics and Theoretical Computer Science29, 129–140, American Mathematical Society Press.

    Google Scholar 

  99. M. Yoeli (1973), Petri Nets and Asynchronous Control Networks. Research Report CS-73-07, Department of Applied Mathematics and Computer Science, University of Waterloo.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. BRICS, Basic Research in Computer Science, Dept. of Computer Science, University of Aarhus, NY Munkegade bld. 540, DK-8000, Århus, C, Denmark

    Mogens Nielsen

  2. Queen Mary and Westfield College, University of London, Mile End Road, E1 4NS, London, UK

    Vladimiro Sassone

Authors
  1. Mogens Nielsen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vladimiro Sassone
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Wolfgang Reisig Grzegorz Rozenberg

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Nielsen, M., Sassone, V. (1998). Petri nets and other models of concurrency. In: Reisig, W., Rozenberg, G. (eds) Lectures on Petri Nets I: Basic Models. ACPN 1996. Lecture Notes in Computer Science, vol 1491. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-65306-6_23

Download citation

  • DOI: https://doi.org/10.1007/3-540-65306-6_23

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65306-6

  • Online ISBN: 978-3-540-49442-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation