Language Compression and Pseudorandom Generators

The language compression problem asks for succinct descriptions of the strings in a language A such that the strings can be efficiently recovered from their description when given a membership oracle for A. We study randomized and nondeterministic decompression schemes and investigate how close we can get to the information theoretic lower bound of log A=n for the description length of strings of length n. Using nondeterminism alone, we can achieve the information theoretic lower bound up to an additive term of O(( log A=n + log n) log n); using both nondeterminism and randomness, we can make do with an excess term of O(log3 n). With randomness alone, we show a lower bound of n − log A=n − O(log n) on the description length of strings in A of length n, and a lower bound of 2 · log A=n − O(1) on the length of any program that distinguishes a given string of length n in A from any other string. The latter lower bound is tight up to an additive term of O(log n). The key ingredient...

• Type: Conference
• Year: 2004
• Where: COCO
• Authors: Harry Buhrman, Troy Lee, Dieter van Melkebeek
• Keywords: COCO 2004, Log A=n, Lower Bound, Theoretic Lower Bound