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» Relativizing Small Complexity Classes and Their Theories
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CSL
2007
Springer
13 years 11 months ago
Relativizing Small Complexity Classes and Their Theories
Existing definitions of the relativizations of NC1 , L and NL do not preserve the inclusions NC1 ⊆ L, NL ⊆ AC1 . We start by giving the first definitions that preserve them....
Klaus Aehlig, Stephen Cook, Phuong Nguyen
COCO
1998
Springer
103views Algorithms» more  COCO 1998»
13 years 9 months ago
Nonrelativizing Separations
We show that MAEXP, the exponential time version of the Merlin-Arthur class, does not have polynomial size circuits. This significantly improves the previous known result due to K...
Harry Buhrman, Lance Fortnow, Thomas Thierauf
ECCC
2008
168views more  ECCC 2008»
13 years 4 months ago
Algebrization: A New Barrier in Complexity Theory
Any proof of P = NP will have to overcome two barriers: relativization and natural proofs. Yet over the last decade, we have seen circuit lower bounds (for example, that PP does n...
Scott Aaronson, Avi Wigderson
JCSS
2006
63views more  JCSS 2006»
13 years 4 months ago
Error-bounded probabilistic computations between MA and AM
We introduce the probabilistic class SBP which is defined in a BPP-like manner. This class emerges from BPP by keeping the promise of a probability gap but decreasing the probabil...
Elmar Böhler, Christian Glaßer, Daniel ...
ECAL
2007
Springer
13 years 11 months ago
Spatial Embedding and Complexity: The Small-World Is Not Enough
The “order for free” exhibited by some classes of system has been exploited by natural selection in order to build systems capable of exhibiting complex behaviour. Here we expl...
Christopher L. Buckley, Seth Bullock