V. Arvind and J. Kobler. Graph isomorphism is low for ZPP NP and other lowness results. Technical Report TR99033, Electronic Colloquium on Computational Complexity, 1999. Home/Search Document Details and Download
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Derandomization and Distinguishing Complexity - Allender, Koucky, Ronneburger.. (2003) (Correct)
....section, it will be helpful to present a technical definition. We begin by recalling the definition of ###P poly#. Definition 26 [5] ###P poly# is the class of languages having an interactive proof system where the strategy of the prover can be computed by a polynomial sized circuit (also see [4] where the multiple prover class MIP#P poly# is observed to be the same as ###P poly#) Clearly ###P poly# # MA # P poly (because Merlin can guess the circuit that implements the Prover s strategy and send send it to Arthur) it appears to be a proper subclass of MA (since otherwise NP # P poly) ....
V. Arvind and J. Kobler. Graph isomorphism is low for ZPP NP and other lowness results. Technical Report TR99033, Electronic Colloquium on Computational Complexity, 1999.
On Higher Arthur-Merlin Classes - Charles, Pavan, Sengupta (Correct)
....attention. Arvind and K obler [AK97] and Goldreich and Zuckerman [GZ97] proved that MA is contained in ZPP NP . K obler and Watanabe [KW95] and Bshouty et al. BCGKT95] proved that the polynomialtime hierarchy is in ZPP NP , if NP has polynomial size circuits. More recently Arvind and K obler [AK00] proved that AM co AM is low for ZPP NP , i.e. ZPP NP AM co AM ZPP NP . We note that this containment is a signi cant improvement over the na ve bound. We consider a generalization of the class AM co AM. Let E k be BP k BP k . We prove NP E1 ZPP NP using the ....
....coincides with the classes we obtained by operators; namely, we can prove the following, given a class of languages C, Proposition 3 AM C = co R NP C = BP NP C . Hence, in particular AM k = BP k 1 . Similarly, given class C, we can de ne the class MA C . Arvind and K obler [AK00] proved a non trivial result about AM co AM. They showed that AM co AM is low for ZPP NP , i.e, ZPP NP AM co AM ZPP NP . Note that a na ve attempt, that just uses the fact AM co AM ZPP NP , yields ZPP NP AM co AM ZPP 2 . Theorem 1 [AK00] For every language L in AM ....
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V. Arvind and J. Kobler, Graph isomorphism is low for ZPP NP and other lowness results, STACS 2000.
On Higher Arthur-Merlin Classes - Charles, Pavan, Sengupta (2000) (Correct)
....attention. Arvind and Kobler [AK97] and Goldreich and Zuckerman [GZ97] proved that MA is contained in ZPP NP . Kobler and Watanabe [KW95] and Bshouty et al. BCGKT95] proved that the polynomialtime hierarchy is in ZPP NP , if NP has polynomial size circuits. More recently Arvind and Kobler [AK00] proved that AM co AM is low for ZPP NP , i.e. ZPP NP AM co AM ZPP NP . We note that this containment is a significant improvement over the naive bound. We consider a generalization of the class AM co AM. Let E k be BP Delta Sigma k BP Delta Pi k . We prove NP E1 ZPP NP ....
....we obtained by operators; namely, we can prove the following, given a class of languages C, Proposition 3 AM C = co R Delta NP C = BP Delta NP C . Hence, in particular AM Sigma k = BP Delta Sigma k 1 . Similarly, given class C, we can define the class MA C . Arvind and Kobler [AK00] proved a non trivial result about AM co AM. They showed that AM co AM is low for ZPP NP , i.e, ZPP NP AM co AM ZPP NP . Note that a naive attempt, that just uses the fact AM co AM ZPP NP , yields ZPP NP AM co AM ZPP Sigma 2 . Theorem 1 [AK00] For every language L in AM ....
[Article contains additional citation context not shown here]
V. Arvind and J. Kobler, Graph isomorphism is low for ZPP NP and other lowness results, STACS 2000.
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V. Arvind and J. Kobler, Graph isomorphism is low for ZPP NP and other lowness results, STACS 2000.
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