Abstract
In the theory of abstract interpretation, we introduce the observational completeness, which extends the common notion of completeness. A domain is complete when abstract computations are as precise as concrete computations. A domain is observationally complete for an observable π when abstract computations are as precise as concrete computations, if we only look at properties in π. We prove that continuity of state-transition functions ensures the existence of the least observationally complete domain. When state-transition functions are additive, the least observationally complete domain boils down to the complete shell.
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References
Birkhoff, G.: Lattice Theory, 3rd edn., vol. XXV. AMS Colloquium Publications, American Mathematical Society (1967)
Cousot, P.: Types as abstract interpretations, invited paper. In: POPL 1997: Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages, pp. 316–331. ACM Press, New York (1997)
Cousot, P., Cousot, R.: Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL 1977: Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages, pp. 238–252. ACM Press, New York (1977)
Cousot, P., Cousot, R.: Systematic design of program analysis frameworks. In: POPL 1979: Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages, pp. 269–282. ACM Press, New York (1979)
Cousot, P., Cousot, R.: Temporal abstract interpretation. In: POPL 2000: Proceedings of the 27th ACM SIGPLAN-SIGACT symposium on Principles of programming languages, pp. 12–25. ACM Press, New York (2000)
Dams, D., Gerth, R., Grumberg, O.: Abstract interpretation of reactive systems. ACM Transactions on Programming Languages and Systems 19(2), 253–291 (1997)
Giacobazzi, R., Quintarelli, E.: Incompleteness, counterexamples, and refinements in abstract model-checking. In: Cousot, P. (ed.) SAS 2001. LNCS, vol. 2126, pp. 356–373. Springer, Heidelberg (2001)
Giacobazzi, R., Ranzato, F., Scozzari, F.: Making abstract interpretations complete. Journal of the ACM 47(2), 361–416 (2000)
Schmidt, D.A.: Comparing completeness properties of static analyses and their logics. In: Kobayashi, N. (ed.) APLAS 2006. LNCS, vol. 4279, pp. 183–199. Springer, Heidelberg (2006)
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Amato, G., Scozzari, F. (2009). Observational Completeness on Abstract Interpretation. In: Ono, H., Kanazawa, M., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2009. Lecture Notes in Computer Science(), vol 5514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02261-6_9
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DOI: https://doi.org/10.1007/978-3-642-02261-6_9
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