We define probabilistic martingales based on randomized approximation schemes, and show that the resulting notion of probabilistic measure has several desirable robustness propert...
We present a notion of resource-bounded measure for P and other subexponential-time classes. This generalization is based on Lutz's notion of measure, but overcomes the limit...
We consider the resource bounded measure of polynomial-time learnable subclasses of polynomial-size circuits. We show that if EXP 6= MA, then every PAClearnable subclass of P=poly...
Ladner [18] showed that there are no minimal recursive sets under polynomial-time reductions. Given any recursive set A, Ladner constructs a set B such that B strictly reduces to ...
We use the powerful tools of counting complexity and generic oracles to help understand the limitations of the complexity of quantum computation. We show several results for the p...
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...
We show that the perfect matching problem is in the complexity class SPL in the nonuniform setting. This provides a better upper bound on the complexity of the matching problem, a...
We show that the satisfiability problem for bounded-error probabilistic ordered branching programs is NP-complete. If the error is very small, however (more precisely, if the erro...