Skip to main content

Arithmetic + logic + geometry = concurrency

  • Conference paper
  • First Online:
LATIN '92 (LATIN 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 583))

Included in the following conference series:

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R.H. Abraham and C.D. Shaw. Dynamics-The Geometry of Behavior. Aerial Press, Inc., Santa Cruz, CA, 1989.

    Google Scholar 

  2. G.D. Birkhoff. Dynamical Systems, volume 9 of Colloquium Publications. American Math. Soc., 1927.

    Google Scholar 

  3. G. Birkhoff. On the combination of subalgebras. Proc. Cambridge Phil. Soc, 29:441–464, 1933.

    Google Scholar 

  4. G. Birkhoff. An extended arithmetic. Duke Mathematical Journal, 3(2), June 1937.

    Google Scholar 

  5. G. Birkhoff. Generalized arithmetic. Duke Mathematical Journal, 9(2), June 1942.

    Google Scholar 

  6. R.T Casley, R.F. Crew, J. Meseguer, and V.R. Pratt. Temporal structures. Math. Structures in Comp. Sci., 1(2):179–213, July 1991.

    Google Scholar 

  7. B. A. Davey and H. A. Priestley. Introduction to Lattices and Order. Cambridge University Press, 1990.

    Google Scholar 

  8. J.-Y. Girard. Linear logic. Theoretical Computer Science, 50:1–102, 1987.

    Google Scholar 

  9. J. Grabowski. On partial languages. Fundamenta Informaticae, IV.2:427–498, 1981.

    Google Scholar 

  10. B. Jonsson. A fully abstract trace model for dataflow networks. In Proc. 16th Annual ACM Symposium on Principles of Programming Languages, pages 155–165, January 1989.

    Google Scholar 

  11. J. Kok. A fully abstract semantics for data flow nets. In Proc. PARLE, II, LNCS 259, pages 351–368. Springer-Verlag, 1987.

    Google Scholar 

  12. M. Nielsen, G. Plotkin, and G. Winskel. Petri nets, event structures, and domains, part I. Theoretical Computer Science, 13, 1981.

    Google Scholar 

  13. C. Papadimitriou. The Theory of Database Control. Computer Science Press, 1986.

    Google Scholar 

  14. G.D. Plotkin and V.R. Pratt. Teams can see pomsets. Manuscript available as pub/pp.tex by anonymous FTP from Boole.Stanford.EDU, October 1988.

    Google Scholar 

  15. V.R. Pratt. Modeling concurrency with partial orders. Int. J. of Parallel Programming, 15(1):33–71, February 1986.

    Google Scholar 

  16. V.R. Pratt. Event spaces and their linear logic. In Proc. Second International Conference on Algebraic Methodology and Software Technology, to appear in 1992, Workshops in Computing, To appear in 1992, Iowa City, 1991. Springer-Verlag.

    Google Scholar 

  17. V.R. Pratt. Modeling concurrency with geometry. In Proc. 18th Ann. ACM Symposium on Principles of Programming Languages, pages 311–322, January 1991.

    Google Scholar 

  18. H.A. Priestley. Representation of distributive lattices. Bull. London Math. Soc., 2:186–190, 1970.

    Google Scholar 

  19. A. Rabinovich and B.A. Trakhtenbrot. Nets of processes and data flow. In Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, REX'88, LNCS 354, pages 574–602, Noordwijkerhout, June 1988. Springer-Verlag.

    Google Scholar 

  20. J. Russel. Full abstraction for nondeterministic dataflow networks. In Proc. 30th IEEE Symposium on Foundations of Computer Science, October 1989.

    Google Scholar 

  21. M. Shields. Deterministic asynchronous automata. In E.J. Neuhold and G. Chroust, editors, Formal Models in Programming. Elsevier Science Publishers, B.V. (North Holland), 1985.

    Google Scholar 

  22. M. Stone. Topological representations of distributive lattices and brouwerian logics. Časopis Pěst. Math., 67:1–25, 1937.

    Google Scholar 

  23. G. Winskel. A category of labelled Petri nets and compositional proof system. In Proc. 3rd Annual Symposium on Logic in Computer Science, Edinburgh, 1988. Computer Society Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Imre Simon

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pratt, V. (1992). Arithmetic + logic + geometry = concurrency. In: Simon, I. (eds) LATIN '92. LATIN 1992. Lecture Notes in Computer Science, vol 583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023846

Download citation

  • DOI: https://doi.org/10.1007/BFb0023846

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55284-0

  • Online ISBN: 978-3-540-47012-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics