Probabilistic Recursion Theory and Implicit Computational Complexity

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 res...

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Bibliographic Details
Published in:Scientific annals of computer science Vol. 24; no. 2; p. 177
Main Authors: Lago, Ugo Dal, Zuppiroli, Sara, Gabbrielli, Maurizio
Format: Journal Article
Language:English
Published: Iasi Alexandru Ioan Cuza University of Iasi 01.01.2014
Subjects:
Complexity
Computation
Cryptography
Mathematical analysis
Mathematical models
Probabilistic methods
Probability theory
Recursion
ISSN:1843-8121, 2248-2695
Online Access:Get full text
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Summary: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.
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ISSN:1843-8121
2248-2695
DOI:10.7561/SACS.2014.2.177