Abstract
One of the fundamental questions in the calculus of communicating processes is determining if a given system of fixed point equations has a solution in the projective model. The present paper provides an approximation principle for the projective model, which makes it posssible to prove assertions in this model by proving them in an infinite sequence of certain finite process algebras. Motivated from this principle a new model for process algebras is defined and its relationship to the projective model is studied.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Arnold, A. and Nivat, M., The Metric Space of Infinite Trees: Algebraic and Topological Properties, Fundamenta Informatica, 3, 4(1980), pp. 445–476.
de Bakker, J. W. and Zucker, J. I., Denotational Semantics of Concurrency, Proceedings 14th STOG, pp. 153–158, 1982.
Bergstra, J. A. and Klop, J. W., Algebra of Communicating Processes, in: Proceedings of the CWI Symposium on Mathematics and Computer Science, J. W. de Bakker, M. Hazenwinkel and J. K. Lenstra, eds., 1986.
Chang, C. C. and Keisler, H. J., Model Theory, North-Holland, 1973.
Dugundji, J., Topology, Allyn and Bacon, 1966.
Dieudonne, J., Elements d’ Analyse, Tom 1, Gauthier-Villars, Paris, 1968.
Eklof. P. C, Ultraproducts for Algebraists, in: Handbook of Mathematical Logic, Barwise, J., ed., pp. 105–137, North-Holland, 1977.
Hoare, C. A. R., Communicating Sequential Processes, Prentice/Hall, 1985.
Kranakis, E., Fixed Point Equations with Parameters in the Projective Model, CWI Technical Report, Computer Science/Department of Algorithms and Architectures, Report GS-R8606, January 1986, to appear.
Lloyd, J., Foundations of Logic Programming, Springer Verlag, 1984.
Milner, R., A Calculus of Communicating Systems, Springer Verlag Lecture Notes in Computer Science, Vol. 92, 1980.
Rounds, W. C, Applications of Topology to Semantics of Communicating Processes, in: Seminar in Concurrency, Springer Verlag Lecture Notes in Computer Science, Vol. 197, 1985, pp. 360–372.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Plenum Press, New York
About this chapter
Cite this chapter
Kranakis, E. (1987). Approximating the Projective Model. In: Skordev, D.G. (eds) Mathematical Logic and Its Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0897-3_19
Download citation
DOI: https://doi.org/10.1007/978-1-4613-0897-3_19
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-8234-1
Online ISBN: 978-1-4613-0897-3
eBook Packages: Springer Book Archive