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 $\frac{1}{2}$ . Analogously, a (less implicit) characterization of the class BPP can be obtained. RSLR is an extensio...

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Bibliographic Details
Published inFoundational and Practical Aspects of Resource Analysis Vol. 7177; pp. 1 - 18
Main Authors Dal Lago, Ugo, Parisen Toldin, Paolo
Format Book Chapter
LanguageEnglish
Published Germany Springer Berlin / Heidelberg 2012
Springer Berlin Heidelberg
SeriesLecture Notes in Computer Science
Subjects
Error Probability
Inference Rule
Normal Form
Polynomial Time
Turing Machine
Online AccessGet full text
ISBN3642324940
9783642324949
ISSN0302-9743
1611-3349
DOI10.1007/978-3-642-32495-6_1

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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 $\frac{1}{2}$ . 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.
Bibliography:Original Abstract: 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac{1}{2}$\end{document}. 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.
ISBN:3642324940
9783642324949
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-642-32495-6_1