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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
Aczel, P.: Non-Well-Founded Sets. CSLI Publication, Stanford, CA (1988)
Bird, R., de Moor, O.: Algebra of Programming. Prentice-Hall, Englewood Cliffs (1997)
Freyd, P., Scedrov, A.: Categories, Allegories. North-Holland, Amsterdam (1990)
Kawahara, Y.: Notes on the universality of relational functors, Memoirs of the Faculty of Science. Kyushu University, vol. 27(3), pp. 275–289 (1973)
Olivier, J.P., Serrato, D.: Catégories de Dedekind. Morphismes dans les Catégories de Schröder. C.R. Acad. Sci. Paris 290, 939–941 (1980)
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)
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)
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)
Winter, M.: A relation algebraic Approach to Interaction Categories. Information Sciences 119, 301–314 (1999)
Winter, M.: A Relation-Algebraic Theory of Bisimulations (submitted to Fundamenta Informatica)
Author information
Authors and Affiliations
Editor information
Rights 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)