• Corpus ID: 15192033

The Role of Relativization in Complexity Theory

@article{Fortnow1994TheRO,
  title={The Role of Relativization in Complexity Theory},
  author={Lance Fortnow},
  journal={Bull. EATCS},
  year={1994},
  volume={52},
  pages={229-243}
}
  • L. Fortnow
  • Published 1994
  • Computer Science
  • Bull. EATCS
Several recent nonrelativizing results in the area of interactive proofs have caused many people to review the importance of relativization. In this paper we take a look at how complexity theorists use and misuse oracle results. We pay special attention to the new interactive proof systems and program checking results and try to understand why they do not relativize. We give some new results that may help us to understand these questions better. 
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88 Citations
Highly Influential Citations
5
Background Citations
19
Methods Citations
4

88 Citations

Relativizing versus Nonrelativizing Techniques: The Role of Local Checkability
TLDR
It is concluded that relativization techniques cannot prove any meaningful restrictions on the power of the principle of local checkability, which is a known proof technique in complexity theory.
Measure One Results in Computational Complexity Theory
TLDR
The examination of relativized complexity theoretic statements which hold for a measure one set of oracles in the measure defined by putting each string into the oracle with probability 1/2 independent of all other strings (a formal definition is given below).
An axiomatic approach to algebrization
TLDR
An axiomatic approach to "algebrization", which complements and clarifies the approaches of [For94] and [AW08], and presents logical theories formalizing the notion of algebrizing techniques in the following sense.
On Complete Problems, Relativizations and Logics for Complexity Classes
  • A. Dawar
  • Mathematics
    Fields of Logic and Computation
  • 2010
TLDR
The question of whether there is a logic capturing P is subject to a relativization barrier is examined and how the question for P differs from those for the other classes by taking a short tour through relativizations, complete problems and recursive enumerations of complexity classes.
Algebrization: A New Barrier in Complexity Theory
TLDR
This article systematically goes through basic results and open problems in complexity theory to delineate the power of the new algebrization barrier, and shows that almost all of the major open problems---including P versus NP, P versus RP, and NEXP versus P/poly---will require non-algebrizing techniques.
Relativized Worlds with an Infinite Hierarchy
Lecture on Relativization
The main result of this lecture is to show the existence of oracles A,B such that P = NP while P 6= NP . A fancy way of expressing this is to say that the P vs. NP question has contradictory…
Nondeterministic Polynomial Time versus Nondeterministic Logartithmic Space
TLDR
The possibility of using the relatively old technique of diagonalization to separate complexity classes, in particular NL from NP, is discussed and several results in this direction are shown.
Nonrelativizing separations
  • H. Buhrman, L. Fortnow, T. Thierauf
  • Mathematics
    Proceedings. Thirteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat. No.98CB36247)
  • 1998
TLDR
It is shown that MA/sub EXP/, the exponential time version of the Merlin-Arthur class, does not have polynomial size circuits and is the first separation result in complexity theory that does not relativize.
Efficient Holographic Proofs
TLDR
It is shown that the recharacterizations of PSPACE in this framework are lamentably unstable, reinforcing the belief that the framework of relativization is incompatible with these new techniques.
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References

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