Abstract
The ambient calculus of Cardelli and Gordon is a process calculus for describing mobile computation where processes may reside within a hierarchy of locations, called ambients. The dynamic semantics of this calculus is presented in a chemical style that allows for a compact and simple formulation. In this semantics, an equivalence relation, called spatial congruence, is defined on the top of an unlabelled transition system.
We show that it is decidable to check whether two ambient calculus processes are spatially congruent or not. This result is based on a natural and intuitive interpretation of ambient processes as edge-labelled unordered trees, which allows us to concentrate on the subtle interaction between two key operators of the ambient calculus, namely restriction, that accounts for the dynamic generation of new location names, and replication, used to encode recursion. The result of our study is the definition of an algorithm to decide spatial congruence and a definition of a normal form for processes that is useful in the proof of important equivalence laws.
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
Martìn Abadi and Andrew D. Gordon. A calculus for cryptographic protocols: the spi calculus. Information and Computation, 148:1–70, 1999.
Gérard Berry and Gérard Boudol. The chemical abstract machine. Theoretical Computer Science, 96:217–248, 1992.
Luca Cardelli and Andrew D. Gordon. Mobile ambients. In Proceedings of FoSSaCS’ 98, volume 1378 of LNCS, pp. 140–155, 1998.
Luca Cardelli and Andrew D. Gordon. Anytime, anywhere: Modal logics for mobile ambients. In Proceedings of POPL’ 00, pp. 365–377, 2000.
Luca Cardelli and Andrew D. Gordon. Logical properties of name restriction. unpublished notes, 2000.
Silvano Dal Zilio. Spatial congruence for the ambients is decidable. Technical Report MSR-TR-2000-41, Microsoft Research, May 2000.
J. Engelfriet and T. Geselma. Multisets and structural congruence of the pi-calculus with replication. Theoretical Computer Science, 211(1-2):311–337, Jan. 1999.
J. Engelfriet and T. Geselma. Structural congruence in the pi-calculus with potential replication. Technical Report 00-02, Leiden Institute of Advanced Computer Science, Jan. 2000.
Andrew D. Gordon and Paul D. Hankin. A concurrent object calculus: reduction and typing. In Proceedings of HLCL’ 98, Elsevier ENTCS, 1998.
Daniel Hirschko.. Mise en oeuvre de preuves de bisimulation. PhD thesis, École Nationale des Ponts et Chaussées, 1999.
Daniel Hirschkoff and Romain Kervarc. Implementation of an algorithm to decide spatial congruence for ambients. LIP, École Normale Supérieure de Lyon, August 2000.
Robin Milner. Flow graphs and flow algebras. Journal of the ACM, 26(4):794–818, Oct. 1979.
Robin Milner. Communicating and Mobile Systems: the Pi-Calculus. Cambridge University Press, 2000.
Vasco T. Vasconcelos. Typed concurrent objects. In Proceedings of ECOOP’ 94, volume 821 of LNCS, pages 100–117, 1994.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dal Zilio, S. (2000). Spatial Congruence for Ambients Is Decidable. In: Jifeng, H., Sato, M. (eds) Advances in Computing Science — ASIAN 2000. ASIAN 2000. Lecture Notes in Computer Science, vol 1961. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44464-5_8
Download citation
DOI: https://doi.org/10.1007/3-540-44464-5_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41428-5
Online ISBN: 978-3-540-44464-0
eBook Packages: Springer Book Archive