Advertisement

Order structures and generalisations of Szpilrajn's theorem

  • Ryszard Janicki
  • Maciej Koutny
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 761)

Abstract

Relational structures of the form (X, R1,R2), with R1R2X × X, R1 being a poset interpreted as causality, R2 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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. 2.
    Anger F.D.: On Lamport's Interprocess Communication Model. ACM TOPLAS 11 (1989), 404–417.Google Scholar
  3. 3.
    Best E., Devillers R.: Concurrent Behaviour: Sequences, Processes and programming Languages. GMD-Studien Nr. 99, GMD, Bonn (1985).Google Scholar
  4. 4.
    Best E., Koutny M.: Petri Net Semantics of Priority Systems. Theoretical Computer Science 94 (1992), 141–158.Google Scholar
  5. 5.
    Fishburn P.C.: Intransitive Indifference with Unequal Indifference Intervals. J. Math. Psych. 7 (1970).Google Scholar
  6. 6.
    Fishburn P.C.: Interval Orders and Interval Graphs. J. Wiley (1985).Google Scholar
  7. 7.
    Fräisse R.: Theory of Relations.North Holland (1986).Google Scholar
  8. 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. 9.
    Gerber R., Lee I.: A Resource-Based Prioritized Bisimulation for Real-Time Systems. Information and Computation, to appear.Google Scholar
  10. 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. 11.
    Janicki R.: A Formal Semantics for Concurrent Systems with a Priority Relation. Acta Informatica 24 (1987), 33–55.Google Scholar
  12. 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. 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. 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. 15.
    Janicki R., Koutny M.: Structure of Concurrency. Theoretical Computer Science 112 (1993), 5–52.Google Scholar
  16. 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. 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. 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. 19.
    Pratt V.: Modelling Concurrency with Partial Orders. Int. Journal of Parallel Programming 15, 1 (1986), 33–71.Google Scholar
  20. 20.
    Szpilrajn E.: Sur l'extension de l'ordre partial. Fundamenta Mathematicae 16 (1930), 386–389.Google Scholar
  21. 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. 22.
    Wiener N.: A Contribution to the Theory of Relative Position. Proc. Camb. Philos. Soc. 17 (1914), 441–449.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Ryszard Janicki
    • 1
  • Maciej Koutny
    • 2
  1. 1.Department of Computer Science and SystemsMcMaster UniversityHamiltonCanada
  2. 2.Department of Computing ScienceUniversity of NewcastleNewcastle upon TyneUK

Personalised recommendations