R. Beigel and B. Fu. Circuits over PP and PL. In IEEE Conference on Computational Complexity, pages 24--35, 1997. Home/Search Document Details and Download
Summary Related Articles Check |
This paper is cited in the following contexts:
The Complexity of Matrix Rank and Feasible Systems of.. - Allender, Beals, Ogihara (1997) (14 citations) (Correct)
....two logspace counting hierarchies, it is tempting to guess that this hierarchy also collapses. Recall that this hierarchy is the class of problems AC 0 reducible to the determinant. Is NC 1 (PL) AC 0 (PL) This question has recently been answered, in the affirmative, by Beigel and Fu [Be95], who also show that NC 1 (PP) AC 0 (PP) Acknowledgments We wish to thank E. Kaltofen and L. Fortnow for insightful comments related to this paper. Dieter van Melkebeek gave useful feedback on an earlier draft. Kousha Ettasimi gave us an exposition of the NL hardness of the Perfect ....
R. Beigel and B. Fu, Circuits over PP and PL. To appear in Proceedings of the 12th Conference on Computational Complexity, 1997.
Isolation, Matching, and Counting: Uniform and.. - Allender, Reinhardt.. (1998) (Correct)
....MV97] By analogy with the class GapP [FFK94] one may define a number of language classes by means of GapL functions. We mention in particular the following three complexity classes, of which the first two have been studied previously. ffl PL = fA : 9f 2 GapL; x 2 A , f(x) 0g (See, e.g. [Gil77, RST84, BCP83, Ogi96, BF97]. ffl C=L = fA : 9f 2 GapL; x 2 A , f(x) 0g [AO96, ABO97, ST94] ffl SPL = fA : A 2 GapLg. It seems that this is the first time that SPL has been singled out for study. In the remainder of this section, we state some of the basic properties of SPL. Proposition 2.1 UL SPL C=L co C=L. ....
R. Beigel and B. Fu. Circuits over PP and PL. In IEEE Conference on Computational Complexity, pages 24--35, 1997.
SIGACT News Complexity Theory Column 19 - Hemaspaandra (1997) (Correct)
....: Delta :#L = AC 0 (#L) the class of problems AC 0 reducible to computing the determinant of integer matrices. The first two of these hierarchies collapse, and they coincide with NC 1 reducibility. ffl AC 0 (C= L) L C=L = NC 1 (C= L) ABO96] ffl AC 0 (PL) PL = NC 1 (PL) [O96, BF97]. These hierarchies are defined using Ruzzo Simon Tompa reducibility [RST] which is the usual notion of oracle access for space bounded nondeterministic Turing machines. It seems natural to conjecture that AC 0 and NC 1 reducibility coincide on #L, too. If they do, then the #L ....
R. Beigel and B. Fu. Circuits over PP and PL. In IEEE Conference on Computational Complexity, pages 24--35, 1997.
Making Nondeterminism Unambiguous - Reinhardt, Allender (1997) (5 citations) (Correct)
.... as well as questions about computing the rank) It is known that some natural hierarchies defined using these complexity classes collapse: ffl AC 0 (C= L) C=L C=L : Delta :C=L = NC 1 (C= L) L C=L [AO96, ABO96] ffl AC 0 (PL) PL PL : Delta :PL = NC 1 (PL) PL [AO96, Ogi96, BF] In contrast, the corresponding #L hierarchy (equal to the class of problems AC 0 reducible to computing the determinant) AC 0 (#L) FL #L : Delta :#L is not known to collapse to any fixed level. Does the equality UL poly = NL poly provide any help in analyzing this hierarchy in the ....
R. Beigel and B. Fu. Circuits over PP and PL. To appear in Proceedings of the 12th Conference on Computational Complexity, 1997.
Making Nondeterminism Unambiguous - Reinhardt, Allender (1998) (5 citations) (Correct)
.... as well as questions about computing the rank) It is known that some natural hierarchies defined using these complexity classes collapse: ffl AC 0 (C= L) C=L C=L : Delta :C=L = NC 1 (C= L) L C=L [AO96, ABO96] ffl AC 0 (PL) PL PL : Delta :PL = NC 1 (PL) PL [AO96, Ogi96, BF97] In contrast, the corresponding #L hierarchy (equal to the class of problems AC 0 reducible to computing the determinant) AC 0 (#L) FL #L : Delta :#L is not known to collapse to any fixed level. Does the equality UL poly = NL poly provide any help in analyzing this hierarchy in the ....
R. Beigel and B. Fu. Circuits over PP and PL. In IEEE Conference on Computational Complexity, pages 24--35, 1997.
The Complexity of Matrix Rank and Feasible Systems of.. - Allender, Beals, Ogihara (1996) (14 citations) (Correct)
....the class of problems AC 0 reducible to the determinant. It is an intriguing question whether NC 1 (PL) AC 0 (PL) The question was open at the moment when the conference version of the present paper was written. Recently, the question has been answered affirmatively by Beigel and Fu [BF97] who also show that NC 1 (PP) AC 0 (PP) Acknowledgments We wish to thank E. Kaltofen and L. Fortnow for insightful comments related to this paper. Dieter van Melkebeek gave useful feedback on an earlier draft. Kousha Ettasimi gave us an exposition of the NL hardness of the Perfect ....
R. Beigel and B. Fu. Circuits over PP and PL. In Proceedings of 11th Computational Complexity, pages 24--35. IEEE Computer Society Press, Los Alamitos, CA, 1997.
Making Nondeterminism Unambiguous - Reinhardt, Allender (1997) (5 citations) (Correct)
No context found.
R. Beigel and B. Fu. Circuits over PP and PL. In IEEE Conference on Computational Complexity, pages 24--35, 1997.
On the Enumerability of the Determinant and the Rank - Alina Beygelzimer Mitsunori (Correct)
No context found.
R. Beigel and B. Fu. Circuits over PP and PL. In 12st IEEE Conference on Computational Complexity, pages 24-35, 1997.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC