Fooling the Parallel Or Tester with Probability 8/27

03/29/2019
by   Jean Goubault-Larrecq, et al.
0

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.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset