Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 41, Number 2 (2000), 142-151.
Complexity of the -query Tautologies in the Presence of a Generic Oracle
Extending techniques of Dowd and those of Poizat, we study computational complexity of in the case when is a generic oracle, where is a positive integer, and denotes the collection of all -query tautologies with respect to an oracle . We introduce the notion of ceiling-generic oracles, as a generalization of Dowd's notion of -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 is not a subset of 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 -generic oracles has Lebesgue measure zero.
Notre Dame J. Formal Logic, Volume 41, Number 2 (2000), 142-151.
First available in Project Euclid: 25 November 2002
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 68Q15: Complexity classes (hierarchies, relations among complexity classes, etc.) [See also 03D15, 68Q17, 68Q19]
Secondary: 03D15: Complexity of computation (including implicit computational complexity) [See also 68Q15, 68Q17]
Suzuki, Toshio. Complexity of the -query Tautologies in the Presence of a Generic Oracle. Notre Dame J. Formal Logic 41 (2000), no. 2, 142--151. doi:10.1305/ndjfl/1038234608. https://projecteuclid.org/euclid.ndjfl/1038234608