A higher-order characterization of probabilistic polynomial time

We present RSLR, an implicit higher-order characterization of the class PP of those problems which can be decided in probabilistic polynomial time with error probability smaller than 12. Analogously, a (less implicit) characterization of the class BPP can be obtained. RSLR is an extension of Hofmann...

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Bibliographic Details
Published in:Information and computation Vol. 241; pp. 114 - 141
Main Authors: Dal Lago, Ugo, Parisen Toldin, Paolo
Format: Journal Article
Language:English
Published: Elsevier Inc 01.04.2015
Elsevier
Subjects:
Computer Science
Implicit computational complexity
Logic in Computer Science
Probabilistic classes
Probabilistic classes
Implicit computational complexity
Linear types
Lambda calculus
ISSN:0890-5401, 1090-2651
Online Access:Get full text
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Summary:We present RSLR, an implicit higher-order characterization of the class PP of those problems which can be decided in probabilistic polynomial time with error probability smaller than 12. Analogously, a (less implicit) characterization of the class BPP can be obtained. RSLR is an extension of Hofmann's SLR with a probabilistic primitive, which enjoys basic properties such as subject reduction and confluence. Polynomial time soundness of RSLR is obtained by syntactical means, as opposed to the standard literature on SLR-derived systems, which use semantics in an essential way.
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2014.10.009