Uniform generation of script N℘-witnesses using an script N℘-oracle

Abstract

A uniform generation procedure for script N℘ is an algorithm that, given any input in a fixed script N℘ -language, outputs a uniformly distributed script N℘ -witness for membership of the input in the language. We present a uniform generation procedure for script N℘ that runs in probabilistic polynomial time with an script N℘ -oracle. This improves upon results of M. Jerrum et al. (1986, Theoret. Comput. Sci. 43, 169-188), which either require a Σ2p oracle or obtain only almost uniform generation. Our procedure utilizes ideas originating in the works of M. Sipser, and L. Stockmeyer (respectively, 1983, in Proceedings of the 15th Annual Symposium on the Theory of Computing, ACM, New York), and Jerrum et al. (1986). © 2000 Academic Press.