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....
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...
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...
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...
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...