Parallel Time and Quantifier Prefixes

. We characterize the amount of alternation between blocks of Boolean quantifiers (having both existential and universal), blocks of real existential quantifiers, and blocks of real universal quantifiers that can be decided in parallel polynomial time over the reals. We do so under the assumption th...

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Bibliographic Details
Published inComputational complexity Vol. 18; no. 4; pp. 527 - 550
Main Authors Cucker, Felipe, de Naurois, Paulin Jacobé
Format Journal Article
LanguageEnglish
Published Basel Birkhäuser-Verlag 01.12.2009
Subjects
Algorithm Analysis and Problem Complexity
Computational Mathematics and Numerical Analysis
Computer Science
68Q15
alternation
complexity classes
parallel time
Quantifier prefixes
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ISSN1016-3328
1420-8954
DOI10.1007/s00037-009-0264-6

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Summary:. We characterize the amount of alternation between blocks of Boolean quantifiers (having both existential and universal), blocks of real existential quantifiers, and blocks of real universal quantifiers that can be decided in parallel polynomial time over the reals. We do so under the assumption that blocks have a uniform bound on their size, both for the case of this bound to be polynomial and constant. On the way towards this characterization we prove a real version of Savitch’s Theorem.
ISSN:1016-3328
1420-8954
DOI:10.1007/s00037-009-0264-6