Citation:
Trevisan, Luca, Salil Vadhan, and David Zuckerman. “Compression of samplable sources.” Computational Complexity: Special Issue on CCC'04 14, no. 3 (2005): 186-227.
CC2005.pdf | 372 KB |
Abstract:
We study the compression of polynomially samplable sources. In particular, we give efficient prefix-free compression and decompression algorithms for three classes of such sources (whose support is a subset of \(\{0, 1\}^n\)).
- We show how to compress sources \(X\) samplable by logspace machines to expected length \(H(X) + O(1)\). Our next results concern flat sources whose support is in \(\mathbf{P}\).
- If \(H(X) ≤ k = n−O(\log n)\), we show how to compress to expected length \(k + \mathrm{polylog}(n − k)\).
- If the support of \(X\) is the witness set for a self-reducible \(\mathbf{NP}\) relation, then we show how to compress to expected length \(H(X)+ 5\).
See also: A Unified Theory of Pseudorandomness (NSF CCF-0133096), Alfred P. Sloan Research Fellowship, Pseudorandomness and Applications (ONR Young Investigator Award; ONR Grant N00014-04-1-0478), Pseudorandomness and Combinatorial Constructions (US-Israel Binational Science Foundation; BSF 2002246)