Abstract
The ambient calculus is a formalism for describing the mobility of both software and hardware. The ambient logic is a modal logic designed to specify properties of distributed and mobile computations programmed in the ambient calculus. In this paper we investigate the border between decidable and undecidable cases of model checking mobile ambients for some fragments of the ambient calculus and the ambient logic.
Recently, Cardelli and Gordon presented a model-checking algorithm for a fragment of the calculus (without name restriction and without replication) against a fragment of the logic (without composition adjunct) and asked the question, whether this algorithm could be extended to include either replication in the calculus or composition adjunct in the logic. Here we answer this question negatively: it is not possible to extend the algorithm, because each of these extensions leads to undecidability of the problem. On the other hand, we extend the algorithm to the calculus with name restriction and logic with new constructs for reasoning about restricted names.
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References
L. Cardelli and G. Ghelli. A query language based on the ambient logic. In Proceedings of the 9th European Symposium on Programming ESOP’01, volume 2028 of LNCS, pages 1–22. Springer, 2001.
L. Cardelli and A. D. Gordon. Equational properties of mobile ambients. In Proceedings FoSSaCS’99, volume 1578 of LNCS, pages 212–226. Springer, 1999. An extended version appears as Microsoft Research Technical Report MSR-TR-99-11, April 1999.
L. Cardelli and A. D. Gordon. Modal logics for mobile ambients: Semantic reasoning. Unpublished annex to [5], 1999.
L. Cardelli and A. D. Gordon. Types for mobile ambients. In Proceedings POPL’99, pages 79–92. ACM, Jan. 1999.
L. Cardelli and A. D. Gordon. Anytime, anywhere: Modal logics for mobile ambients. In Proceedings POPL’00, pages 365–377. ACM, Jan. 2000.
L. Cardelli and A. D. Gordon. Mobile ambients. Theoretical Computer Science, 240(1):177–213, 2000.
L. Cardelli and A. D. Gordon. Logical properties of name restriction. In Proceedings of the 5th International Conference on Typed Lambda Calculi and Applications (TLCA’01), volume 2044 of LNCS, pages 46–60. Springer, 2001.
W. Charatonik, S. Dal Zilio, A. D. Gordon, S. Mukhopadhyay, and J.-M. Talbot. The complexity of model checking mobile ambients. In Proceedings FoSSaCS’01, volume 2030 of LNCS, pages 152–167. Springer, 2001.
S. Dal Zilio. Spatial congruence for ambients is decidable. In Proceedings of the 6th Asian Computing Science Conference (ASIAN’00), volume 1961 of LNCS, pages 88–103. Springer, 2000. A full version Technical Report MSR-TR-2000-57, Microsoft Research.
E. L. Post. Recursively Enumerable Sets of Positive Integers and their Decision Problems. Bulletion of the American Mathematical Society, 50:284–316, 1944.
D. Sangiorgi. Extensionality and intensionality of the ambient logics. In Proceedings POPL’01, pages 4–13. ACM, Jan. 2001.
B. A. Trakhtenbrot. The impossibility of an algorithm for the decision problem for finite models. Doklady Akademii Nauk SSR, 70:569–572, 1950.
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Charatonik, W., Talbot, JM. (2001). The Decidability of Model Checking Mobile Ambients. In: Fribourg, L. (eds) Computer Science Logic. CSL 2001. Lecture Notes in Computer Science, vol 2142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44802-0_24
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DOI: https://doi.org/10.1007/3-540-44802-0_24
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