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

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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.

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  1. Department of Mathematics and Information Sciences, Osaka Prefecture University, Sakai, Osaka, 599-8531, Japan

    Toshio Suzuki

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  1. Toshio Suzuki
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Correspondence to Toshio Suzuki.

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The author was partially supported by Grant-in-Aid for Scientific Research (No. 14740082), Japan Society for the Promotion of Science.

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Suzuki, T. Bounded truth table does not reduce the one-query tautologies to a random oracle. Arch. Math. Logic 44, 751–762 (2005). https://doi.org/10.1007/s00153-005-0283-1

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