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http://dspace.mediu.edu.my:8181/xmlui/handle/1721.1/6115Full metadata record
| DC Field | Value | Language |
|---|---|---|
| dc.creator | Minsky, Marvin | - |
| dc.creator | Papert, Seymour | - |
| dc.date | 2004-10-04T14:39:54Z | - |
| dc.date | 2004-10-04T14:39:54Z | - |
| dc.date | 1964-11-01 | - |
| dc.date.accessioned | 2013-10-09T02:43:04Z | - |
| dc.date.available | 2013-10-09T02:43:04Z | - |
| dc.date.issued | 2013-10-09 | - |
| dc.identifier | AIM-073 | - |
| dc.identifier | http://hdl.handle.net/1721.1/6115 | - |
| dc.identifier.uri | http://koha.mediu.edu.my:8181/xmlui/handle/1721 | - |
| dc.description | When is a set A of positive integers, represented as binary numbers, "regular" in the sense that it is a set of sequences that can be recognized by a finite-state machine? Let pie A(n) be the number of members of A less than the integer n. It is shown that the asymptotic behavior of pie A(n) is subject to severe restraints if A is regular. These constraints are violated by many important natural numerical sets whose distribution functions can be calculated, at least asymptotically. These include the set P of prime numbers for which pie P(n)~n/log n for large n, the set of integers A (k) of the form n to the power k for which pie A(k)(n)1/k, and many others. The technique cannot, however, yield a decision procedure for regularity since for every infinite regular set A there is a nonregular set A for which /pie Z(n)-pie A(n)/is less than or equal to 1, so that the asymptotic behaviors of the two distribution functions are essentially identical. | - |
| dc.format | 1711310 bytes | - |
| dc.format | 217016 bytes | - |
| dc.format | application/postscript | - |
| dc.format | application/pdf | - |
| dc.language | en_US | - |
| dc.relation | AIM-073 | - |
| dc.title | Unrecognizable Sets of Numbers | - |
| Appears in Collections: | MIT Items | |
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