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2000 Complexity of the $r$-query Tautologies in the Presence of a Generic Oracle
Toshio Suzuki
Notre Dame J. Formal Logic 41(2): 142-151 (2000). DOI: 10.1305/ndjfl/1038234608


Extending techniques of Dowd and those of Poizat, we study computational complexity of $r\mathit{TAUT}[A]$ in the case when $A$ is a generic oracle, where $r$ is a positive integer, and $r\mathit{TAUT}[A]$ denotes the collection of all $r$-query tautologies with respect to an oracle $A$. We introduce the notion of ceiling-generic oracles, as a generalization of Dowd's notion of $t$-generic oracles to arbitrary finitely testable arithmetical predicates. We study how existence of ceiling-generic oracles affects behavior of a generic oracle, by which we show that $\{ X: co\mathit{NP}[X] $ is not a subset of $\mathit{NP}[r\mathit{TAUT}[X]]\}$ is comeager in the Cantor space. Moreover, using ceiling-generic oracles, we present an alternative proof of the fact (Dowd) that the class of all $t$-generic oracles has Lebesgue measure zero.


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Toshio Suzuki. "Complexity of the $r$-query Tautologies in the Presence of a Generic Oracle." Notre Dame J. Formal Logic 41 (2) 142 - 151, 2000.


Published: 2000
First available in Project Euclid: 25 November 2002

zbMATH: 1015.03045
MathSciNet: MR1932226
Digital Object Identifier: 10.1305/ndjfl/1038234608

Primary: 68Q15
Secondary: 03D15

Keywords: computational complexity , generic oracle , random oracle , t-generic oracle

Rights: Copyright © 2000 University of Notre Dame


Vol.41 • No. 2 • 2000
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