Skip to main content

An Ordered Category of Processes

  • Conference paper
Book cover Relations and Kleene Algebra in Computer Science (RelMiCS 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4988))

Included in the following conference series:

Abstract

Processes can be seen as relations extended in time. In this paper we want to investigate this observation by deriving an ordered category of processes. We model processes as co-algebras of a relator on Dedekind category up to bisimilarity. On those equivalence classes we define a lower semi-lattice structure and a monotone composition operation.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abramsky, S., Gay, S., Nagarajan, R.: Interaction Categories and the Foundations of Typed Concurrent Programming. In: Broy, M. (ed.) Proceedings of the 1994 Marktoberdorf Summer School on Deductive Program Design, pp. 35–113. Springer, Heidelberg (1996)

    Google Scholar 

  2. Aczel, P.: Non-Well-Founded Sets. CSLI Publication, Stanford, CA (1988)

    Google Scholar 

  3. Bird, R., de Moor, O.: Algebra of Programming. Prentice-Hall, Englewood Cliffs (1997)

    MATH  Google Scholar 

  4. Freyd, P., Scedrov, A.: Categories, Allegories. North-Holland, Amsterdam (1990)

    MATH  Google Scholar 

  5. Kawahara, Y.: Notes on the universality of relational functors, Memoirs of the Faculty of Science. Kyushu University, vol. 27(3), pp. 275–289 (1973)

    Google Scholar 

  6. Olivier, J.P., Serrato, D.: Catégories de Dedekind. Morphismes dans les Catégories de Schröder. C.R. Acad. Sci. Paris 290, 939–941 (1980)

    MATH  MathSciNet  Google Scholar 

  7. Olivier, J.P., Serrato, D.: Squares and Rectangles in Relational Categories - Three Cases: Semilattice, Distributive lattice and Boolean Non-unitary. Fuzzy sets and systems 72, 167–178 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  8. Schmidt, G., Ströhlein, T.: Relationen und Graphen. Springer, Heidelberg (1989); English version: Relations and Graphs. Discrete Mathematics for Computer Scientists, EATCS Monographs on Theoret. Comput. Sci., Springer (1993)

    MATH  Google Scholar 

  9. Schmidt, G., Hattensperger, C., Winter, M.: Heterogeneous Relation Algebras. In: Brink, C., Kahl, W., Schmidt, G. (eds.) Relational Methods in Computer Science. Advances in Computer Science, Springer, Heidelberg (1997)

    Google Scholar 

  10. Winter, M.: A relation algebraic Approach to Interaction Categories. Information Sciences 119, 301–314 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  11. Winter, M.: A Relation-Algebraic Theory of Bisimulations (submitted to Fundamenta Informatica)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Rudolf Berghammer Bernhard Möller Georg Struth

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Winter, M. (2008). An Ordered Category of Processes. In: Berghammer, R., Möller, B., Struth, G. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2008. Lecture Notes in Computer Science, vol 4988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78913-0_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-78913-0_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78912-3

  • Online ISBN: 978-3-540-78913-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics