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Information complexity of online problems. (English) Zbl 1287.68083

Hliněný, Petr (ed.) et al., Mathematical foundations of computer science 2010. 35th international symposium, MFCS 2010, Brno, Czech Republic, August 23–27, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-15154-5/pbk). Lecture Notes in Computer Science 6281, 24-36 (2010).
Summary: What is information? Frequently spoken about in many contexts, yet nobody has ever been able to define it with mathematical rigor. The best we are left with so far is the concept of entropy by Shannon, and the concept of information content of binary strings by Chaitin and Kolmogorov. While these are doubtlessly great research instruments, they are hardly helpful in measuring the amount of information contained in particular objects. In a pursuit to overcome these limitations, we propose the notion of information content of algorithmic problems. We discuss our approaches and their possible usefulness in understanding the basic concepts of informatics, namely the concept of algorithms and the concept of computational complexity.
For the entire collection see [Zbl 1194.68039].

MSC:

68Q30 Algorithmic information theory (Kolmogorov complexity, etc.)
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