On automated verification of probabilistic programs

Axel Legay, Andrzej S. Murawski, Joël Ouaknine, and James Worrell

We introduce a simple procedural probabilistic programming language which is suitable for coding a wide variety of randomised algorithms and protocols. This language is interpreted over finite datatypes and has a decidable equivalence problem. We have implemented an automated equivalence checker, which we call APEX, for this language, based on game semantics. We illustrate our approach with three non-trivial case studies: (i) Herman's self-stabilisation algorithm; (ii) an analysis of the average shape of binary search trees obtained by certain sequences of random insertions and deletions; and (iii) the problem of anonymity in the Dining Cryptographers protocol. In particular, we record an exponential speed-up in the latter over state-of-the-art competing approaches.

Proceedings of TACAS 08, LNCS 4963, 2008. 15 pages.

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