Skip to main content
SpringerLink
Log in

Order structures and generalisations of Szpilrajn's theorem

  • Conference paper
  • First Online:
Foundations of Software Technology and Theoretical Computer Science (FSTTCS 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 761))

Abstract

Relational structures of the form (X, R 1,R 2), with R 1 ⫅R 2 ⫅ X × X, R 1 being a poset interpreted as causality, R 2 being interpreted as ‘not later than’ or ‘weak causality’ relation, are considered. Szpilrajn's theorem that each poset is the intersection of its total extensions is generalised to such structures; the interpretation and applications of the results obtained are discussed.

Supported by NSERC grant, No. OGP 0036539.

Supported by Esprit Basic Research Working Group 6067 CALIBAN

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. Abraham U., Ben-David S., Magidor M.: On Global-Time and Inter-Process Communication.In: Semantics for Concurrency — Leicester 1990, Workshops in Computing, Springer-Verlag (1990), 311–323.

    Google Scholar 

  2. Anger F.D.: On Lamport's Interprocess Communication Model. ACM TOPLAS 11 (1989), 404–417.

    Google Scholar 

  3. Best E., Devillers R.: Concurrent Behaviour: Sequences, Processes and programming Languages. GMD-Studien Nr. 99, GMD, Bonn (1985).

    Google Scholar 

  4. Best E., Koutny M.: Petri Net Semantics of Priority Systems. Theoretical Computer Science 94 (1992), 141–158.

    Google Scholar 

  5. Fishburn P.C.: Intransitive Indifference with Unequal Indifference Intervals. J. Math. Psych. 7 (1970).

    Google Scholar 

  6. Fishburn P.C.: Interval Orders and Interval Graphs. J. Wiley (1985).

    Google Scholar 

  7. Fräisse R.: Theory of Relations.North Holland (1986).

    Google Scholar 

  8. Gaifman H., Pratt V.: Partial Order Models of Concurrency and the Computation of Function. Proc. of Symposium on Logic in Computer Science (1987), 72–25.

    Google Scholar 

  9. Gerber R., Lee I.: A Resource-Based Prioritized Bisimulation for Real-Time Systems. Information and Computation, to appear.

    Google Scholar 

  10. van Glabbeek R., Vaandrager F.: Petri Net Models for Algebraic Theories of Concurrency. Proc. of PARLE'87, Lecture Notes in Computer Science 259 (1987), 224–242.

    Google Scholar 

  11. Janicki R.: A Formal Semantics for Concurrent Systems with a Priority Relation. Acta Informatica 24 (1987), 33–55.

    Google Scholar 

  12. Janicki R., Koutny M.: Observing Concurrent Histories. in: Proceedings of Real-Time Systems, Theory and Applications, York 1989, H.M.S. Zedan (Ed.), Elsevier Science Publishers B.V. (North-Holland) (1990), 133–142.

    Google Scholar 

  13. Janicki R., Koutny M.: Invariants and Paradigms of Concurrency Theory. Proc. of PARLE'91, Lecture Notes in Computer Science 506 (1991), 59–74.

    Google Scholar 

  14. Janicki R., Koutny M.: Invariant Semantics of Nets with Inhibitor Arcs. Proc. of CONCUR'91, Lecture Notes in Computer Science 527 (1991), 317–331.

    Google Scholar 

  15. Janicki R., Koutny M.: Structure of Concurrency. Theoretical Computer Science 112 (1993), 5–52.

    Google Scholar 

  16. Lamport L.: The Mutual Exclusion problem: Part I-A Theory of Interprocess Communication; Part II — Statements and Solutions. Journal of the ACM 33 (1986), 313–326.

    Google Scholar 

  17. Nielsen M., Engberg U., Larsen K.S.: Fully Abstract Models for a Process Language with Refinement. Lecture Notes in Computer Science 354, Springer (1988), 523–548.

    Google Scholar 

  18. Plotkin G., Pratt V.: Teams Can See Pomsets. unpublished memo, available electronically as pub/pp2.tex by anonymous FTP from Boole.Stanford.EDU.

    Google Scholar 

  19. Pratt V.: Modelling Concurrency with Partial Orders. Int. Journal of Parallel Programming 15, 1 (1986), 33–71.

    Google Scholar 

  20. Szpilrajn E.: Sur l'extension de l'ordre partial. Fundamenta Mathematicae 16 (1930), 386–389.

    Google Scholar 

  21. Vogler W.: Failure Semantics Based on Interval Semiwords is a Congruence for Refinement. Proc. of STACS'90, Lecture Notes in Computer Science 415, Springer (1990), 285–297.

    Google Scholar 

  22. Wiener N.: A Contribution to the Theory of Relative Position. Proc. Camb. Philos. Soc. 17 (1914), 441–449.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Systems, McMaster University, L8S 4K1, Hamilton, Ontario, Canada

    Ryszard Janicki

  2. Department of Computing Science, University of Newcastle, NE1 7RU, Newcastle upon Tyne, UK

    Maciej Koutny

Authors
  1. Ryszard Janicki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Maciej Koutny
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Rudrapatna K. Shyamasundar

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Janicki, R., Koutny, M. (1993). Order structures and generalisations of Szpilrajn's theorem. In: Shyamasundar, R.K. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1993. Lecture Notes in Computer Science, vol 761. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57529-4_68

Download citation

  • DOI: https://doi.org/10.1007/3-540-57529-4_68

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57529-0

  • Online ISBN: 978-3-540-48211-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation