Fooling the Parallel or Tester with Probability 8/27

  • Jean Goubault-LarrecqEmail author
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11760)


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.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.LSV, ENS Paris-Saclay, CNRS, Université Paris-SaclayCachanFrance

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