Abstract
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.
This work was partially supported by ETH grant TH 18 07-3, and APVV grant 0433-06.
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References
Böckenhauer, H.-J., Komm, D., Královič, R., Královič, R., Mömke, T.: Online algorithms with advice. Technical Report 614, ETH Zürich (2009)
Böckenhauer, H.-J., Komm, D., Královič, R., Královič, R., Mömke, T.: On the advice complexity of online problems. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 331–340. Springer, Heidelberg (2009)
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)
Chaitin, G.J.: On the length of programs for computing finite binary sequences. Journal of the ACM 13(4), 547–569 (1966)
Dobrev, S., Královič, R., Pardubská, D.: How much information about the future is needed? In: Geffert, V., Karhumäki, J., Bertoni, A., Preneel, B., Návrat, P., Bieliková, M. (eds.) SOFSEM 2008. LNCS, vol. 4910, pp. 247–258. Springer, Heidelberg (2008)
Emek, Y., Fraigniaud, P., Korman, A., Rosén, A.: Online computation with advice. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S.E., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5555, pp. 427–438. Springer, Heidelberg (2009)
Hromkovič, J.: Design and Analysis of Randomized Algorithms: Introduction to Design Paradigms, Texts in Theoretical Computer Science. An EATCS Series. Springer, New York (2005)
Hromkovič, J., Mömke, T., Steinhöfel, K., Widmayer, P.: Job shop scheduling with unit length tasks: bounds and algorithms. Algorithmic Operations Research 2(1), 1–14 (2007)
Kolmogorov, A.N.: Three approaches to the definition of the concept “quantity of information”. Problemy Peredachi Informatsii 1, 3–11 (1965)
Shannon, C.E.: A mathematical theory of communication. Mobile Computing and Communications Review 5(1), 3–55 (2001)
Turing, A.M.: On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society 2(42), 230–265 (1936)
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Hromkovič, J., Královič, R., Královič, R. (2010). Information Complexity of Online Problems. In: Hliněný, P., Kučera, A. (eds) Mathematical Foundations of Computer Science 2010. MFCS 2010. Lecture Notes in Computer Science, vol 6281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15155-2_3
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DOI: https://doi.org/10.1007/978-3-642-15155-2_3
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