Combinatorics, complexity, and randomness

Combinatorics, Complexity, and Randomness, 1985

Richard M. Karp, of the University of California-Berkeley, received the 1985 ACM A. M. Taring Award for his fundamental contributions to complexity theory. Presented at the Association's Annual Conference in Denver, Colorado, in October, the award is ACM's highest honor in computer science research. By 1972, Karp had established a reputation as one of the world's leading computer science theori...

Algorithmic Randomness and Complexity

Complexity and Randomness

2 Random finite strings 7 2.1 Plain Kolmogorov complexity . . . . . . . . . . . . . . . . . . 7 2.2 Prefix-free complexity . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Kraft inequality, Shannon-Fano code . . . . . . . . . . . . . . 9 2.4 The universal semimeasure m . . . . . . . . . . . . . . . . . . 10 2.5 A priori probability . . . . . . . . . . . . . . . . . . . . . . . . 11 2.6 Coding,...

Randomness and Complexity

Kolmogorov Complexity and Algorithmic Randomness

This paper aims to provide a minimal introduction to algorithmic randomness. In particular, we cover the equivalent 1-randomness and MartinLöf randomness. After a brief review of relevant concepts in computability, we develop the basic theory of Kolmogorov complexity, including the KC theorem and more general notion of information content measures. We then build two natural definitions of rando...