Time-space tradeoffs in the counting hierarchy

Extends the lower-bound techniques of L. Fortnow (2000) to the unbounded-error probabilistic model. A key step in the argument is a generalization of V.A. Nepomnjas/spl caron/c/spl caron/ii/spl breve/'s (1970) theorem from the Boolean setting to the arithmetic setting. This generalization is made possible due to the recent discovery of logspace-uniform TC/sup 0/ circuits for iterated multiplication (A. Chiu et al., 2000). As an example of the sort of lower bounds that we obtain, we show that MAJ-MAJSAT is not contained in PrTiSp(n/sup 1+o(1)/, n/sup /spl epsiv//) for any /spl epsiv/