Abstract
It is well-known that the higher-order language PCF is not fully abstract: there is a program—the so-called parallel or tester, meant to test whether its input behaves as a parallel or—which never terminates on any input, operationally, but is denotationally non-trivial. We explore a probabilistic variant of PCF, and ask whether the parallel or tester exhibits a similar behavior there. The answer is no: operationally, one can feed the parallel or tester an input that will fool it into thinking it is a parallel or. We show that the largest probability of success of such would-be parallel ors is exactly 8/27. The bound is reached by a very simple probabilistic program. The difficult part is to show that that bound cannot be exceeded.
This research was partially supported by Labex DigiCosme (project ANR-11-LABEX-0045-DIGICOSME) operated by ANR as part of the program “Investissement d’Avenir” Idex Paris-Saclay (ANR-11-IDEX-0003-02).
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Goubault-Larrecq, J. (2019). Fooling the Parallel or Tester with Probability 8/27. In: Alvim, M., Chatzikokolakis, K., Olarte, C., Valencia, F. (eds) The Art of Modelling Computational Systems: A Journey from Logic and Concurrency to Security and Privacy. Lecture Notes in Computer Science(), vol 11760. Springer, Cham. https://doi.org/10.1007/978-3-030-31175-9_18
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