Archive for Mathematical Logic

, Volume 44, Issue 6, pp 751–762 | Cite as

Bounded truth table does not reduce the one-query tautologies to a random oracle

Article

Abstract

The relativized propositional calculus is a system of Boolean formulas with query symbols. A formula in this system is called a one-query formula if the number of occurrences of query symbols is just one. If a one-query formula is a tautology with respect to a given oracle A then it is called a one-query tautology with respect to A. By extending works of Ambos-Spies (1986) and us (2002), we investigate the measure of the class of all oracles A such that the set of all one-query tautologies with respect to A does not p-btt-reduce to A, where p-btt denotes polynomial-time bounded-truth-table. We show that certain Dowd-type generic oracles all belong to the class, and hence measure of the class is one.

Keywords or phrases

Dowd-type generic oracle Measure One-query tautology Random oracle The relativized propositional calculus Truth table reduction 

Mathematics Subject Classification (2000)

68Q15 03D15 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of Mathematics and Information SciencesOsaka Prefecture UniversitySakaiJapan

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