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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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Rochester, NY
1989
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| Series: | University of Rochester <Rochester, NY> / Department of Computer Science: Technical report
286 |
| Subjects: | |
| Summary: | 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." |
| Physical Description: | 20 S. |
Staff View
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| 490 | 1 | |a University of Rochester <Rochester, NY> / Department of Computer Science: Technical report |v 286 | |
| 520 | 3 | |a 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." | |
| 650 | 4 | |a Computational complexity | |
| 650 | 4 | |a Random fields | |
| 700 | 1 | |a Wechsung, Gerd |d 1939- |e Verfasser |0 (DE-588)122393384 |4 aut | |
| 810 | 2 | |a Department of Computer Science: Technical report |t University of Rochester <Rochester, NY> |v 286 |w (DE-604)BV008902697 |9 286 | |
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Record in the Search Index
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| author | Hemachandra, Lane A. Wechsung, Gerd 1939- |
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| indexdate | 2024-07-09T17:27:17Z |
| institution | BVB |
| language | English |
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| publishDate | 1989 |
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| series2 | University of Rochester <Rochester, NY> / Department of Computer Science: Technical report |
| spelling | Hemachandra, Lane A. Verfasser aut Using randomness to characterize the complexity of computation Lane A. Hemachandra ; Gerd Wechsung Rochester, NY 1989 20 S. txt rdacontent n rdamedia nc rdacarrier University of Rochester <Rochester, NY> / Department of Computer Science: Technical report 286 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." Computational complexity Random fields Wechsung, Gerd 1939- Verfasser (DE-588)122393384 aut Department of Computer Science: Technical report University of Rochester <Rochester, NY> 286 (DE-604)BV008902697 286 |
| spellingShingle | Hemachandra, Lane A. Wechsung, Gerd 1939- Using randomness to characterize the complexity of computation Computational complexity Random fields |
| title | Using randomness to characterize the complexity of computation |
| title_auth | Using randomness to characterize the complexity of computation |
| title_exact_search | Using randomness to characterize the complexity of computation |
| title_full | Using randomness to characterize the complexity of computation Lane A. Hemachandra ; Gerd Wechsung |
| title_fullStr | Using randomness to characterize the complexity of computation Lane A. Hemachandra ; Gerd Wechsung |
| title_full_unstemmed | Using randomness to characterize the complexity of computation Lane A. Hemachandra ; Gerd Wechsung |
| title_short | Using randomness to characterize the complexity of computation |
| title_sort | using randomness to characterize the complexity of computation |
| topic | Computational complexity Random fields |
| topic_facet | Computational complexity Random fields |
| volume_link | (DE-604)BV008902697 |
| work_keys_str_mv | AT hemachandralanea usingrandomnesstocharacterizethecomplexityofcomputation AT wechsunggerd usingrandomnesstocharacterizethecomplexityofcomputation |