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We give a new characterization of NP: the class NP contains exactly those languages L for which membership proofs (a proof that an input x is in L) can be verified probabilisticall...
Abstract Summary of results The subcubic (O(n ) for < 3) algorithms to multiply Boolean matrices do not provide the witnesses; namely, they compute C = AB but if Cij = 1 they d...
We describe dynamic data structures for half-space range reporting and for maintaining the minima of a decomposable function. Using these data structures, we obtain efficient dyna...
We introduce the notion of empty alternation by investigating alternating automata which are restricted to empty their storage except for a logarithmically space-bounded tape befor...