Using randomness to characterize the complexity of computation
Abstract: "Kolmogorov complexity -- the study of the randomness of strings -- has developed into a fundamental tool in proving lower bounds in computation and in constructing oracles separating complexity classes. In this paper, we show that Kolmogorov complexity is a central tool in the unders...
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| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Rochester, NY
1989
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| Schriftenreihe: | University of Rochester <Rochester, NY> / Department of Computer Science: Technical report
286 |
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| Zusammenfassung: | Abstract: "Kolmogorov complexity -- the study of the randomness of strings -- has developed into a fundamental tool in proving lower bounds in computation and in constructing oracles separating complexity classes. In this paper, we show that Kolmogorov complexity is a central tool in the understanding of deterministic and nondeterministic complexity classes and hierarchies; we show that many collapses of computational complexity classes can be completely characterized in terms of Kolmogorov complexity. We discuss P, NP, unique polynomial time, the polynomial hierarchy, and the exponential hierarchy. We show that, for many complexity classes C, C equals a smaller complexity class unless some language in C is accepted only by machines whose execution creates computational structures with a non-trivial degree of randomness. Our fundamental proof technique is a divide and conquer scheme on the tree of potential computational structures." |
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| Beschreibung: | 20 S. |