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**Generalized theorems on relationships among reducibility notions to certain complexity classes.**
*(English)*
Zbl 0813.68105

The author shows that if a class is closed under either (I) NP many-one reductions and polynomial-time conjunctive reductions or (II) coNP many- one reductions and polynomial-time disjunctive reductions, then reducibility notions of sets from the class under polynomial-time constant-round truth-table reducibility, polynomial-time log-Turing reducibility, logspace constant-round truth-table reducibility, logspace log-Turing reducibility, and logspace Turing reducibility are all equivalent and the class is also closed under polynomial-time positive Turing reductions.

Reviewer: Du Ding-Zhu (Minneapolis)

### MSC:

68Q15 | Complexity classes (hierarchies, relations among complexity classes, etc.) |

03D15 | Complexity of computation (including implicit computational complexity) |

### Keywords:

reducibility### References:

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