- Author:
- Osamu Watanabe
There are many ways to measure the complexity of a given object, but there are two measures of particular importance in the theory of computing: One is Kolmogorov complexity, which measures the amount of information necessary to describe an object. Another is computational complexity, which measures the computational resources necessary to recognize (or produce) an object. The relation between these two complexity measures has been studied since the 1960s. More recently, the more generalized notion of resource bounded Kolmogorov complexity and its relation to computational complexity have received much attention. Now many interesting and deep observations on this topic have been established. This book consists of four survey papers concerning these recent studies on resource bounded Kolmogorov complexity and computational complexity. It also contains one paper surveying several types of Kolmogorov complexity measures. The papers are based on invited talks given at the AAAI Spring Symposium on Minimal-Length Encoding in 1990. The book is the only collection of survey papers on this subject and provides fundamental information for researchers in the field.
Cited By
- Ribeiro M, Lazzaretti A and Lopes H (2018). A study of deep convolutional auto-encoders for anomaly detection in videos, Pattern Recognition Letters, 105:C, (13-22), Online publication date: 1-Apr-2018.
- Schmidhuber J (2015). Deep learning in neural networks, Neural Networks, 61:C, (85-117), Online publication date: 1-Jan-2015.
Recommendations
The pervasive reach of resource-bounded Kolmogorov complexity in computational complexity theory
We continue an investigation into resource-bounded Kolmogorov complexity (Allender et al., 2006 [4]), which highlights the close connections between circuit complexity and Levin's time-bounded Kolmogorov complexity measure Kt (and other measures with a ...