Extraction rates of algorithmically random continuous functionals: Extraction rates of...: D. Cenzer et al.
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| Title: | Extraction rates of algorithmically random continuous functionals: Extraction rates of...: D. Cenzer et al. |
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| Authors: | Cenzer, Douglas1 (AUTHOR) cenzer@ufl.edu, Fraize, Cameron1 (AUTHOR) cameron.fraize@ufl.edu, Porter, Christopher2 (AUTHOR) christopher.porter@drake.edu |
| Source: | Natural Computing. Mar2025, Vol. 24 Issue 1, p17-28. 12p. |
| Subjects: | Algorithmic randomness, Distribution (Probability theory), Recursion theory, Functionals, Trees |
| Abstract: | In this article, we study the extraction rate, or output/input rate, of continuous functionals on the Cantor space 2 ω , in particular for algorithmically random functionals. It is shown that random functionals have an average extraction rate over all inputs corresponding to the rate of producing a single bit of output, and that this average rate is attained for any sufficiently random input. We also examine functionals computed by discrete distribution generating trees, where we calculate the expected extraction rate and show that this rate is attained for any sufficiently random input. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | In this article, we study the extraction rate, or output/input rate, of continuous functionals on the Cantor space 2 ω , in particular for algorithmically random functionals. It is shown that random functionals have an average extraction rate over all inputs corresponding to the rate of producing a single bit of output, and that this average rate is attained for any sufficiently random input. We also examine functionals computed by discrete distribution generating trees, where we calculate the expected extraction rate and show that this rate is attained for any sufficiently random input. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 15677818 |
| DOI: | 10.1007/s11047-024-10000-x |
