Notre Dame Journal of Formal Logic

Forcing Complexity: Minimum Sizes of Forcing Conditions

Toshio Suzuki

Abstract

This note is a continuation of our former paper ''Complexity of the r-query tautologies in the presence of a generic oracle.'' We give a very short direct proof of the nonexistence of t-generic oracles, a result obtained first by Dowd. We also reconstitute a proof of Dowd's result that the class of all r-generic oracles in his sense has Lebesgue measure one.

Article information

Source
Notre Dame J. Formal Logic, Volume 42, Number 2 (2001), 117-120.

Dates
First available in Project Euclid: 5 June 2003

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1054837938

Digital Object Identifier
doi:10.1305/ndjfl/1054837938

Mathematical Reviews number (MathSciNet)
MR1993395

Zentralblatt MATH identifier
1060.03065

Subjects
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]

Keywords
computational complexity t-generic oracle

Citation

Suzuki, Toshio. Forcing Complexity: Minimum Sizes of Forcing Conditions. Notre Dame J. Formal Logic 42 (2001), no. 2, 117--120. doi:10.1305/ndjfl/1054837938. https://projecteuclid.org/euclid.ndjfl/1054837938


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References

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  • [2] Dowd, M., "Generic oracles, uniform machines, and codes", Information and Computation, vol. 96 (1992), pp. 65–76.
  • [3] Poizat, B., “$\mathcal{Q}=\mathcal{NQ}$?” The Journal of Symbolic Logic, vol. 51 (1986), pp. 22–32.
  • [4] Suzuki, T., "Recognizing tautology by a deterministic algorithm whose while-loop's execution time is bounded by forcing", Kobe Journal of Mathematics, vol. 15 (1998), pp. 91–102.
  • [5] Suzuki, T., Computational Complexity of Boolean Formulas with Query Symbols, Ph.D. thesis, University of Tsukuba, Tsukuba-City, 1999.
  • [6] Suzuki, T., "Complexity of the $r$"-query tautologies in the presence of a generic oracle, Notre Dame Journal of Formal Logic, vol. 41 (2000), pp. 142–151.
  • [7] Suzuki, T., "Degrees of Dowd-type generic oracles", Information and Computation, vol. 176 (2002), pp. 66–87.