Probabilistic Autoreductions

@inproceedings{Zhang2016ProbabilisticA,
  title={Probabilistic Autoreductions},
  author={Liyu Zhang and Chen Yuan and Haibin Kan},
  booktitle={SOFSEM},
  year={2016}
}
We consider autoreducibility of complete sets for the two common types of probabilistic polynomial-time reductions: RP reductions containing one-sided errors on positive input instances only, and BPP reductions containing two-sided errors. Specifically, we focus on the probabilistic counterparts of the deterministic many-one and truth-table autoreductions. We prove that non-trivial complete sets of NP are autoreducible for the RP many-one reduction. This extends the result by Glaβer et al. [9… 
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References

SHOWING 1-10 OF 21 REFERENCES
Using autoreducibility to separate complexity classes
TLDR
It is shown that all Turing complete sets for exponential space are autoreducible but there exists some Turing complete set for doubly exponential space that is not, and a separation of logarithmic space from polynomial space is got.
Non-autoreducible Sets for NEXP
TLDR
It is shown that under some polynomial-time reductions there are complete sets for NEXP that are not autoreducible and settled the question whether every complete set for N EXP under non-adaptative reduction is autore Ducible under NOR-truth-table reduction.
On being incoherent without being very hard
TLDR
All NP-complete sets are coherent, and new lower bounds onprogram checkability andrandom-self-reducibility are obtained on behalf of Yao and by Blum and Kannan.
Three results on the polynomial isomorphism of complete sets
  • J. Goldsmith, D. Joseph
  • Mathematics
    27th Annual Symposium on Foundations of Computer Science (sfcs 1986)
  • 1986
TLDR
This paper proves three results relating to the isomorphism question for NP-complete sets, showing that no simple modification of the diagonalization argument used by Ko, Long and Du can be used to produce sets that are both EXPtime-complete w.r.t, polynomial many-one reducibility and not p-isomorphic.
NP is as easy as detecting unique solutions
TLDR
It is shown that the problems of distinguishing between instances of SAT having zero or one solution, or finding solutions to instances of SOTA having unique solutions, are as hard as SAT itself.
Computability and Complexity Theory
TLDR
Conise, focused materials cover the most fundamental concepts and results in the field of modern complexity theory, including the theory of NP-completeness, NP-hardness, the polynomial hierarchy, and complete problems for other complexity classes.
On the structure of complete sets
  • H. Buhrman, L. Torenvliet
  • Mathematics
    Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory
  • 1994
TLDR
In this expository paper, the progress that has been made in recent years on selected topics in the study of complete sets is reviewed.
Bounded Query Classes
TLDR
The Boolean hierarchy is generalized in such a way that it is possible to characterize P and O in terms of the generalization, and the class $P^{\text{NP}}[O(\log n)]$ can be characterized in very different ways.
A Post's Program for Complexity Theory
TLDR
This work proposes a program for the separation of complexity classes and identifies three properties that are potential separators: auto-reducibility, robustness, and mitoticity.
Splitting NP-Complete Sets
TLDR
It is demonstrated that complete sets share a redundancy that was not known before, and the equivalence between autoreducibility and mitoticity for all polynomial-time-bounded reducibilities between 3-tt- reducibility and Turing-reducibility is disproved.
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