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Distinguishing conjunctive and disjunctive reducibilities by sparse sets. (English) Zbl 0681.68066
Summary: Various polynomial-time truth-table reducibilities are compared by their ability of using sparse oracles to answer queries. The reducibilities studied here include conjunctive reducibility, bounded conjunctive reducibility, disjunctive reducibility, bounded disjunctive reducibility, truth-table reducibility, and bounded truth-table reducibility. For any two reducibilities $$\leq^ P_ r$$ and $$\leq^ P_ s$$, we compare the class of sets $$\leq^ P_ r$$-reducible to sparse sets with the class of sets $$\leq^ P_ s$$-reducible to sparse sets. For most pairs of reducibilities $$\leq^ P_ r$$ and $$\leq^ P_ s$$, it is shown that the two associated reduction classes are incomparable, unless a trivial inclusive relation holds.

##### MSC:
 68Q25 Analysis of algorithms and problem complexity 03D15 Complexity of computation (including implicit computational complexity) 68Q05 Models of computation (Turing machines, etc.) (MSC2010)
##### Keywords:
oracle machines; reducibilities; sparse sets
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