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.
Dal Lago, U., Zuppiroli, S., Gabbrielli, M. (2014). Probabilistic recursion theory and implicit computational complexity. SCIENTIFIC ANNALS OF COMPUTER SCIENCE, 24(2), 177-216 [10.7561/SACS.2014.2.177].
Probabilistic recursion theory and implicit computational complexity
DAL LAGO, UGO;ZUPPIROLI, SARA;GABBRIELLI, MAURIZIO
2014
Abstract
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.File in questo prodotto:
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