Probabilistic quantifiers and games
type: Item
instance of: scholarly article
title: Probabilistic quantifiers and games
zbMATH Open document ID: 0659.03024
DOI: 10.1016/0022-0000(88)90037-2
author: Stathis Zachos
published in: Journal of Computer and System Sciences
publication date: 1988-01-01T00:00:00Z
review text: A characterization of classical complexity classes (both deterministic and probabilistic) in terms of the ordinary quantifiers \(\exists\) and \(\forall\) together with a quantifier \(\exists^+\), which means roughly ``for most'', is given. Quantifier-swapping principles are presented that reduce many class-inclusion and hierarchy-collapse proofs to straightforward algebraic manipulations. Examples of theorems subsumed by such an approach are: (i) the containment of BPP in the second level of the polynomial hierarchy and (ii) the collapse of the Arthur-Merlin hierarchy to its second level. The paper also includes a chart of class- inclusion and oracle-based separation results.
reviewed by: Stasys Jukna
Mathematics Subject Classification ID: 03D15
Mathematics Subject Classification ID: 68Q25
zbMATH DE Number: 4077190
zbMATH Keywords: probabilistic computations
zbMATH Keywords: complexity hierarchies
zbMATH Keywords: complexity classes
zbMATH Keywords: BPP
zbMATH Keywords: polynomial hierarchy
zbMATH Keywords: Arthur-Merlin hierarchy
Wikidata QID: Q60060632
MaRDI profile type: Publication
full work available at URL: 0022-0000(88)90037-2
OpenAlex ID: W2072242455
cites work: On counting problems and the polynomial-time hierarchy
cites work: Relative to a Random OracleA, ${\bf P}^A \ne {\bf NP}^A \ne \text{co-}{\bf NP}^A $ with Probability 1
cites work: Relativizations of the $\mathcal{P} = ?\mathcal{NP}$ Question
cites work: A second step toward the polynomial hierarchy
cites work: Does co-NP have short interactive proofs ?
cites work: Q4720789
cites work: Computational Complexity of Probabilistic Turing Machines
cites work: Q4198056
cites work: The knowledge complexity of interactive proof-systems
cites work: On relativized exponential and probabilistic complexity classes
cites work: Q3715098
cites work: Some observations on the probabilistic algorithms and NP-hard problems
cites work: BPP and the polynomial hierarchy
cites work: The complexity of facets (and some facets of complexity)
cites work: Probabilistic algorithm for testing primality
cites work: Relativized Questions Involving Probabilistic Algorithms
cites work: The polynomial-time hierarchy
cites work: Q4302454
cites work: A Fast Monte-Carlo Test for Primality
cites work: Complete sets and the polynomial-time hierarchy
cites work: Robustness of probabilistic computational complexity classes under definitional perturbations
cites work: Q3768891
cites work: Q3792245
cites work: A decisive characterization of BPP
DBLP publication ID: journals/jcss/Zachos88
description: scientific article; zbMATH DE number 4077190