Probabilistic Recursion Theory and Implicit Computational Complexity

Ugo Dal Lago, Sara Zuppiroli, Maurizio Gabbrielli
2014 Scientific Annals of Computer Science  
We show that probabilistic computable functions, i.e., those functions outputting distributions and computed by probabilistic Turing machines, can be characterized by a natural generalization of Church and Kleene's partial recursive functions. The obtained algebra, following Leivant, can be restricted so as to capture the notion of a polytime sampleable distribution, a key concept in average-case complexity and cryptography.
doi:10.7561/sacs.2014.2.177 fatcat:whd4wlyi7jcdpljt6ekodurize