The Swendsen-Wang process provides one possible dynamics (an ergodic Markov chain) for the Q-state Potts model in statistical physics. Computer simulations of this process are widely used to estimate the expectations of various observable (random variables) of a Potts system in the equilibrium (or Gibbs) distribution. The legitimacy of such simulations… (More)
A quasi-polynomial-time algorithm is presented for sampling almost uniformly at random from the n-slice of the language L(G) generated by an arbitrary context-free grammar G. (The n-slice of a language L over an alphabet is the subset L\ n of words of length exactly n.) The time complexity of the algorithm is " ?2 (n jGj) O(log n) , where the parameter "… (More)
We show that uniform families of ACC circuits of subexponential size cannot compute the permanent function. This also implies similar lower bounds for certain sets in PP. This is one of the very few examples of a lower bound in circuit complexity whose proof hinges on the uniformity condition; it is still unknown if there is any set in Ntime (2 n O(1)) that… (More)
We show that log-bounded rudimentary reductions (deened and studied by Jones in 1975) characterize Dlogtime-uniform AC 0 .
3 A preliminary version of this paper appeared as [AG91a]. 1 SUMMARY As part of a study of almost-everywhere complex sets, we investigate sets that are immune to AC 0 ; that is, sets with no innite subset in AC 0. We show that such sets exist in P PP and in DSPACE(log n log 3 n). Our main result is an oracle construction indicating that any improvement in… (More)